186 results
Search Results
2. Error estimates of variational discretization for semilinear parabolic optimal control problems
- Author
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Zuliang Lu, Xuejiao Chen, Chunjuan Hou, and Fei Huang
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,Type (model theory) ,semilinear parabolic equations ,Residual ,Optimal control ,lcsh:QA1-939 ,Backward Euler method ,Omega ,Finite element method ,error estimates ,optimal control problems ,A priori and a posteriori ,Applied mathematics ,finite element methods ,Mathematics - Abstract
In this paper, variational discretization directed against the optimal control problem governed by nonlinear parabolic equations with control constraints is studied. It is known that the a priori error estimates is $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h+k)$ using backward Euler method for standard finite element. In this paper, the better result $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h^2+k)$ is gained. Beyond that, we get a posteriori error estimates of residual type.
- Published
- 2021
3. On the extinction of continuous-state branching processes in random environments
- Author
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Xiangqi Zheng
- Subjects
education.field_of_study ,Extinction ,extinction ,General Mathematics ,lcsh:Mathematics ,Population ,branching processes ,Asymptotic distribution ,State (functional analysis) ,virus ,lcsh:QA1-939 ,epidemic ,Branching (linguistics) ,Distribution (mathematics) ,Transformation (function) ,Quantitative Biology::Populations and Evolution ,Statistical physics ,asymptotic behavior ,time-space transformation ,education ,Epidemic model ,Mathematics - Abstract
This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Levy random environments. Some results on extinction are presented, including the distribution of the extinction time, the limiting distribution conditioned on large extinction times and the asymptotic behavior near extinction. This paper also provides a new time-space transformation which can be used for further exploration in similar models. The results are applied to an epidemic model to describe the dynamics of infectious population and a virus model to describe the dynamics of viral load.
- Published
- 2021
4. New escape conditions with general complex polynomial for fractals via new fixed point iteration
- Author
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Yu-Pei Lv, Sumaira Nawaz, Muhammad Tanveer, Ali Raza, and Imran Ahmed
- Subjects
General Mathematics ,lcsh:Mathematics ,State (functional analysis) ,Fixed point ,Mandelbrot set ,lcsh:QA1-939 ,mandelbrot set ,Fractal ,Quadratic equation ,fractal ,fixed point ,Fixed-point iteration ,Scheme (mathematics) ,general polynomial ,Applied mathematics ,Orbit (control theory) ,Mathematics ,multi-corns set - Abstract
The aim of this paper is to generalize the results regarding fractals and prove escape conditions for general complex polynomial. In this paper we state the orbit of a newly defined iterative scheme and establish the escape criteria in fractal generation for general complex polynomial. We use established escape criteria in algorithms to generate Mandelbrot and Multi-corns sets. In addition, we present some graphs of quadratic, cubic and higher Mandelbrot and Multi-corns sets and discuss how the alteration in parameters make changes in graphs.
- Published
- 2021
5. Oscillation theorems for higher order dynamic equations with superlinear neutral term
- Author
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Jehad Alzabut, Kamaleldin Abodayeh, and Said R. Grace
- Subjects
Class (set theory) ,Oscillation ,General Mathematics ,lcsh:Mathematics ,Applied mathematics ,Order (group theory) ,oscillation criteria ,higher order dynamic equations ,lcsh:QA1-939 ,Dynamic equation ,superlinear neutral term ,Term (time) ,Mathematics - Abstract
In this paper, several oscillation criteria for a class of higher order dynamic equations with superlinear neutral term are established. The proposed results provide a unified platform that adequately covers both discrete and continuous equations and further sufficiently comments on oscillatory behavior of more general class of equations than the ones reported in the literature. We conclude the paper by demonstrating illustrative examples.
- Published
- 2021
6. Interval neutrosophic covering rough sets based on neighborhoods
- Author
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Huaxiang Xian, Dongsheng Xu, and Xiewen Lu
- Subjects
Discrete mathematics ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,lcsh:Mathematics ,covering rough sets ,Interval (mathematics) ,Mathematical proof ,lcsh:QA1-939 ,Bridge (interpersonal) ,interval neutrosophic sets ,neutrosophic sets ,rough sets ,Rough set ,Mathematics ,neighborhood - Abstract
Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets.
- Published
- 2021
7. Numerical simulation of the fractal-fractional reaction diffusion equations with general nonlinear
- Author
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Manal Alqhtani and Khaled M. Saad
- Subjects
Computer simulation ,Differential equation ,lagrange polynomial interpolation ,General Mathematics ,lcsh:Mathematics ,the fractal-fractional reaction diffusion equations ,lcsh:QA1-939 ,Fractal dimension ,Nonlinear system ,the exponential law ,Fractal ,Kernel (statistics) ,Reaction–diffusion system ,the power law ,Applied mathematics ,Exponential decay ,generalized mittag-leffler function ,Mathematics - Abstract
In this paper a new approach to the use of kernel operators derived from fractional order differential equations is proposed. Three different types of kernels are used, power law, exponential decay and Mittag-Leffler kernels. The kernel's fractional order and fractal dimension are the key parameters for these operators. The main objective of this paper is to study the effect of the fractal-fractional derivative order and the order of the nonlinear term, 1
- Published
- 2021
8. Strongly essential set of vector Ky Fan's points problem and its applications
- Author
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Dejin Zhang, Yan-Long Yang, Shu-Wen Xiang, and Xicai Deng
- Subjects
Pure mathematics ,Current (mathematics) ,General Mathematics ,lcsh:Mathematics ,Solution set ,hausdorff upper semimetric ,lcsh:QA1-939 ,vector ky fan's points ,Set (abstract data type) ,Section (fiber bundle) ,multiobjective games ,Component (UML) ,strong essential component ,ky fan's section problems ,weakly pareto-nash equilibrium ,Point (geometry) ,strong essential set ,Mathematics - Abstract
In this paper, several existence results of strongly essential set of the solution set for Ky Fan's section problems and vector Ky Fan's point problems are obtained. Firstly, two kinds of strongly essential sets of Ky Fan's section problems are defined, and some further results on existence of the strongly essential component of solutions set of Ky Fan's section problems are proved, which generalize the conclusion in [ 22 ], and further generalize the conclusions in [ 21 , 28 ]. Secondly, based on the above results, two classes of stronger perturbations of vector-valued inequality functions are proposed respectively, and several existence results of the strongly essential component of set of vector Ky Fan's points are obtained. By comparing several metrics, we give some strong and weak relationships among the various metrics involved in the text. The main results of this paper actually generalize the relevant conclusions in the current literature. Finally, as an application, we obtain an existence result of the strongly essential component of weakly Pareto-Nash equilibrium for multiobjective games.
- Published
- 2021
9. Locally finiteness and convolution products in groupoids
- Author
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Joseph Neggers, Hee Sik Kim, and In Ho Hwang
- Subjects
Pure mathematics ,moebius function ,General Mathematics ,interval value function ,lcsh:Mathematics ,above ,locally finite ,below ,groupoid ,lcsh:QA1-939 ,convolution product ,Riemann zeta function ,zeta function ,symbols.namesake ,Number theory ,Special functions ,Lattice (order) ,symbols ,transitive interval property ,Mathematics - Abstract
In this paper, we introduce a version of the Moebius function and other special functions on a particular class of intervals for groupoids, and study them to obtain results analogous to those obtained in the usual lattice, combinatorics and number theory setting, but of course much more general due to the viewpoint taken in this paper.
- Published
- 2020
10. Role of shape operator in warped product submanifolds of nearly cosymplectic manifolds
- Author
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Rifaqat Ali, Nadia Alluhaibi, Fatemah Mofarreh, Khaled Mohamed Khedher, and Wan Ainun Mior Othman
- Subjects
Pure mathematics ,General Mathematics ,lcsh:Mathematics ,Mathematics::History and Overview ,Physics::Optics ,Submanifold ,characterizations ,lcsh:QA1-939 ,Computer Science::Computers and Society ,Computer Science::Computer Vision and Pattern Recognition ,Shape operator ,integrability conditions ,Mathematics::Differential Geometry ,Invariant (mathematics) ,shape operators ,warped product ,Mathematics - Abstract
In this paper, first, we find the integrability theorems for the invariant and slant distributions which appeared in the concept of semi-slant submanifolds. Utilizing these theorems, we prove that a semi-slant submanifold reduces to be a warped product semi-slant submanifold, provided some necessary and sufficient conditions concerning the shape operators. Also, it is shown that a few earlier results are exceptional cases of this paper results.
- Published
- 2020
11. The new reflected power function distribution: Theory, simulation & application
- Author
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Riffat Jabeen, Ahmad Saeed Akhter, and Azam Zaka
- Subjects
Percentile ,Distribution (number theory) ,reflected power function distribution ,General Mathematics ,lcsh:Mathematics ,Order statistic ,Truncated mean ,Estimator ,power function distribution ,Function (mathematics) ,percentile estimator ,lcsh:QA1-939 ,characterization of truncated distribution ,Applied mathematics ,Applied science ,Power function ,Mathematics - Abstract
The aim of the paper is to propose a new Reflected Power function distribution (RPFD). We provide the various properties of the new model in detail such as moments, vitality function and order statistics. We characterize the RPFD based on conditional moments (Right and Left Truncated mean) and doubly truncated mean. We also study the shape of the new distribution to be applicable in many real life situations. We estimate the parameters for the proposed RPFD by using different methods such as maximum likelihood method, modified maximum likelihood method, percentile estimator and modified percentile estimator. The aim of the study is to increase the application of the Power function distribution (PFD). Using two different data sets from real life, we conclude that the RPFD perform better as compare to different competitor models already exist in the literature. We hope that the findings of this paper will be useful for researchers in different field of applied sciences.
- Published
- 2020
12. The existence of solutions and generalized Lyapunov-type inequalities to boundary value problems of differential equations of variable order
- Author
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Lei Hu and Shuqin Zhang
- Subjects
Lyapunov function ,Differential equation ,General Mathematics ,lcsh:Mathematics ,existence ,derivatives and integrals of variable order ,lcsh:QA1-939 ,differential equations of variable order ,piecewise constant functions ,symbols.namesake ,Nonlinear system ,Schauder fixed point theorem ,generalized lyapunov-type inequality ,symbols ,Piecewise ,Applied mathematics ,Boundary value problem ,Constant function ,Mathematics ,Variable (mathematics) - Abstract
In this paper, we discuss the existence of solutions to a boundary value problem of differential equations of variable order, which is a piecewise constant function. Our results are based on the Schauder fixed point theorem. Then, under some assumptions on the nonlinear term, we obtain a generalized Lyapunov-type inequality to the two-point boundary value problem considered. To the best of our knowledge, there is no paper dealing with Lyapunov-type inequalities for boundary value problems in term of variable order. In addition, some examples of the obtained inequalities are given.
- Published
- 2020
13. Solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type
- Author
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Yilin Wang, Yibing Sun, Yige Zhao, and Zhi Liu
- Subjects
General Mathematics ,lcsh:Mathematics ,existence ,Existence theorem ,Fixed-point theorem ,Type (model theory) ,Expression (computer science) ,Differential operator ,Lipschitz continuity ,lcsh:QA1-939 ,mixed perturbations ,Banach algebra ,boundary value problem ,fractional differential equation ,Applied mathematics ,Boundary value problem ,Mathematics - Abstract
In this paper, we consider the solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type. The expression of the solution for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is discussed based on the definition and the property of the Caputo differential operators. By the fixed point theorem in Banach algebra due to Dhage, an existence theorem for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is given under mixed Lipschitz and Caratheodory conditions. As an application, an example is presented to illustrate the main results. Our results in this paper extend and improve some well-known results. To some extent, our work fills the gap on some basic theory for the boundary value problems of fractional differential equations with mixed perturbations of the second type involving Caputo differential operator.
- Published
- 2020
14. Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order
- Author
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Hatice Tuǧba Yolcu and Erhan Deniz
- Subjects
Subordination (linguistics) ,Pure mathematics ,Polynomial ,starlike functions ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,subordination ,faber polynomial ,lcsh:QA1-939 ,bi-univalent functions ,Complex order ,analytic functions ,meromorphic functions ,Polynomial coefficients ,Analytic function ,Mathematics ,Meromorphic function - Abstract
In this paper, we obtain the upper bounds for the n-th (n ≥ 1) coefficients for meromorphic bi-subordinate functions of complex order by using Faber polynomial expansions. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
- Published
- 2020
15. Asymptotic stability of degenerate stationary solution to a system of viscousconservation laws in half line
- Author
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Tohru Nakamura
- Subjects
Conservation law ,General Mathematics ,lcsh:Mathematics ,Degenerate energy levels ,Mathematical analysis ,Perturbation (astronomy) ,stationary waves| boundary layer solutions| compressible viscous gases| energy method| center manifold theory ,A priori estimate ,Half-space ,lcsh:QA1-939 ,Standing wave ,Exponential stability ,A priori and a posteriori ,Mathematics - Abstract
In this paper, we study a system of viscous conservation laws given by a form of a symmetricparabolic system. We consider the system in the one-dimensional half space and show existence ofa degenerate stationary solution which exists in the case that one characteristic speed is equal to zero.Then we show the uniform a priori estimate of the perturbation which gives the asymptotic stability ofthe degenerate stationary solution. The main aim of the present paper is to show the a priori estimatewithout assuming the negativity of non-zero characteristics. The key to proof is to utilize the Hardyinequality in the estimate of low order terms.
- Published
- 2018
16. Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow
- Author
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Ayaka Matsubara and Tomomi Yokota
- Subjects
Picard–Lindelöf theorem ,General Mathematics ,coupled sound and heat flow|monotone operators|the Hille-Yosida theorem|existence|uniqueness|regularity of solutions ,lcsh:Mathematics ,Mathematical analysis ,lcsh:QA1-939 ,Domain (mathematical analysis) ,symbols.namesake ,Homogeneous ,Dirichlet boundary condition ,Bounded function ,symbols ,Uniqueness ,Hille–Yosida theorem ,Heat flow ,Mathematics - Abstract
This paper deals with the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain Ω in RN, with homogeneous Dirichlet boundary conditions. Existence and uniqueness of solutions to the problem are established by using the Hille-Yosida theorem. This paper gives a simpler proof than one by Carasso (1975). Moreover, regularity of solutions is established.
- Published
- 2016
17. The Meir-Keeler type contractions in extended modular b-metric spaces with an application
- Author
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Manuel De la Sen, Shaban Sedghi, Ozgur Ege, Abdolsattar Gholidahneh, Zoran D. Mitrović, and Ege Üniversitesi
- Subjects
Discrete mathematics ,extended modular metric space ,triangular fuzzy p-metric space ,business.industry ,General Mathematics ,lcsh:Mathematics ,Fixed-point theorem ,Mathematics::General Topology ,Fixed point ,Type (model theory) ,Modular design ,Space (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,alpha-nu-Meir-Keeler contraction ,Metric space ,$ \alpha $-$ \widehat{\nu} $-meir-keeler contraction ,integral equation ,fixed point ,Graph (abstract data type) ,business ,Mathematics - Abstract
In this paper, we introduce the notion of a modular p-metric space (an extended modular b-metric space) and establish some fixed point results for alpha-nu-Meir-Keeler contractions in this new space. Using these results, we deduce some new fixed point theorems in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Also, we develop an important relation between fuzzy-Meir-Keeler and extended fuzzy p-metric with modular p-metric and get certain new fixed point results in triangular fuzzy p-metric spaces. We provide an example and an application to support our results which generalize several well known results in the literature., Basque GovernmentBasque Government [IT1207-19]; Ege University Scientific Research Projects Coordination UnitEge University [FGA-2020-22080], The authors would like to thank the editor and the anonymous referees for their careful reading of our manuscript and their many insightful comments and suggestions. The authors thank the Basque Government for its support of this work through Grant IT1207-19. This study is supported by Ege University Scientific Research Projects Coordination Unit. Project Number FGA-2020-22080.
- Published
- 2021
18. Closure properties of generalized λ-Hadamard product for a class of meromorphic Janowski functions
- Author
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Huo Tang, Tao He, Shu-Hai Li, and Lina Ma
- Subjects
Subordination (linguistics) ,Pure mathematics ,Class (set theory) ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,hadamard product ,generalized λ-hadamard product ,janowski functions ,Function (mathematics) ,Lambda ,lcsh:QA1-939 ,closure property ,Closure (mathematics) ,Product (mathematics) ,Hadamard product ,meromorphic function ,Meromorphic function ,Mathematics - Abstract
In this paper, we introduce a class of meromorphic starlike function by subordination relationship and generalized $\lambda$-Hadamard product. We obtain the necessary and sufficient conditions and closure properties of the class. In addition, some new results of the class are given.
- Published
- 2021
19. On the stability of two functional equations for (S,N)-implications
- Author
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Dapeng Lang, Xinyu Han, Sizhao Li, and Songsong Dai
- Subjects
Stability study ,General Mathematics ,lcsh:Mathematics ,functional equations ,stability ,lcsh:QA1-939 ,Fuzzy logic ,Stability (probability) ,humanities ,Combinatorics ,(s,n)-implication ,law of importation ,iterative boolean-like law ,Product (mathematics) ,fuzzy implications ,Functional equation ,Beta (velocity) ,Law of importation ,Fuzzy negation ,Mathematics - Abstract
The iterative functional equation $ \alpha\rightarrow(\alpha\rightarrow \beta) = \alpha\rightarrow \beta $ and the law of importation $ (\alpha\wedge \beta)\rightarrow \gamma = \alpha\rightarrow (\beta\rightarrow \gamma) $ are two tautologies in classical logic. In fuzzy logics, they are two important properties, and are respectively formulated as $ I(\alpha, \beta) = I(\alpha, I(\alpha, \beta)) $ and $ I(T(\alpha, \beta), \gamma) = I(\alpha, I(\beta, \gamma)) $ where $ I $ is a fuzzy implication and $ T $ is a $ t $-norm. Over the past several years, solutions to these two functional equations involving different classes of fuzzy implications have been studied. However, there are no results about stability study of fuzzy functional equations involving fuzzy implication. This paper discusses fuzzy implications that do not strictly satisfying these equations, but approximately satisfy these equations. Then we establish the Hyers-Ulam stability of the iterative functional equation involving the $ (S, N) $-implication, where the $ (S, N) $-implication is a common class of fuzzy implications generated by a continuous $ t $-conorm $ S $ and a continuous fuzzy negation $ N $. Furthermore, given a fixed $ t $-norm (the minimum $ t $-norm or the product $ t $-norm) the Hyers-Ulam stability of the law of importation involving the $ (S, N) $-implication is studied.
- Published
- 2021
20. Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial b-metric space
- Author
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Pragati Gautam, Vishnu Narayan Mishra, Swapnil Verma, and Rifaqat Ali
- Subjects
Pure mathematics ,quasi-partial b-metric space ,General Mathematics ,lcsh:Mathematics ,Fixed-point theorem ,qpb-cyclic chatterjea contraction mapping ,Fixed point ,cyclic mapping ,lcsh:QA1-939 ,Complete metric space ,interpolation ,Metric space ,chatterjea contraction ,fixed point ,Uniqueness ,Contraction (operator theory) ,Mathematics - Abstract
The fixed point results for Chatterjea type contraction in the setting of Complete metric space exists in literature. Taking this approach forward Karapinar gave the concept of cyclic Chatterjea contraction mappings. Fan also worked on these cyclic mappings in a new setting of quasi-partial b-metric space. Motivated by the work of these researchers, we have introduced the notion of $qp_{b}$-cyclic Chatterjea contractive mappings and established fixed point results on them. The aim of this paper is to use an interpolative approach in the framework of quasi-partial b-metric space and to prove existence and uniqueness of fixed point theorem for $qp_{b}$-interpolative Chatterjea contraction mappings. The results are affirmed with applications based on them.
- Published
- 2021
21. New iterative approach for the solutions of fractional order inhomogeneous partial differential equations
- Author
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Rashid Nawaz, Sumbal Ahsan, Kottakkaran Sooppy Nisar, Dumitru Baleanu, and Laiq Zada
- Subjects
Partial differential equation ,Laplace transform ,Iterative method ,General Mathematics ,lcsh:Mathematics ,fractional order inhomogeneous system ,Interval (mathematics) ,fractional calculus ,lcsh:QA1-939 ,approximate solutions ,Fractional calculus ,Transformation (function) ,Integer ,fractional order roseau-hyman equation ,Applied mathematics ,Decomposition method (constraint satisfaction) ,new iterative method ,Mathematics - Abstract
In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0, 1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations.
- Published
- 2021
22. Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings
- Author
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J. F. Tang, X. R. Wang, M. Liu, S. S. Chang, and Salahuddin
- Subjects
residual gap function ,General Mathematics ,lcsh:Mathematics ,Hausdorff space ,Solution set ,Inverse ,hausdorff lipschitz continuity ,Monotonic function ,Function (mathematics) ,error bounds ,Lipschitz continuity ,Residual ,relaxed monotonicity ,lcsh:QA1-939 ,generalized f-projection operator ,regularized gap function ,Variational inequality ,Applied mathematics ,generalized vector inverse quasi-variational inequality problems ,global gap function ,bi-mapping ,Mathematics ,strong monotonicity - Abstract
The goal of this paper is further to study a kind of generalized vector inverse quasi-variational inequality problems and to obtain error bounds in terms of the residual gap function, the regularized gap function, and the global gap function by utilizing the relaxed monotonicity and Hausdorff Lipschitz continuity. These error bounds provide effective estimated distances between an arbitrary feasible point and the solution set of generalized vector inverse quasi-variational inequality problems.
- Published
- 2021
23. Generating bicubic B-spline surfaces by a sixth order PDE
- Author
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Yan Wu and Chun-Gang Zhu
- Subjects
Surface (mathematics) ,Partial differential equation ,bicubic b-spline surfaces ,Basis (linear algebra) ,General Mathematics ,B-spline ,pde surfaces ,lcsh:Mathematics ,Mathematical analysis ,sixth order pde ,lcsh:QA1-939 ,Mathematics::Numerical Analysis ,PDE surface ,Computer Science::Graphics ,Bicubic interpolation ,Boundary value problem ,Representation (mathematics) ,Mathematics - Abstract
As the solutions of partial differential equations (PDEs), PDE surfaces provide an effective way for physical-based surface design in surface modeling. The bicubic B-spline surface is a useful tool for surface modeling in computer aided geometric design (CAGD). In this paper, we present a method for generating bicubic B-spline surfaces with the uniform knots and the quasi-uniform knots from the sixth order PDEs. From the given boundary condition, based on the cubic B-spline basis representation and the PDE mask, the resulting bicubic B-spline surface can be generated uniquely. The boundary condition is more flexible and can be applied for curvature-continuous surface design, surface blending and hole filling. Some representative examples show the effectiveness of the presented method.
- Published
- 2021
24. The stationary distribution of a stochastic rumor spreading model
- Author
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Dapeng Gao, Peng Guo, and Chaodong Chen
- Subjects
Lyapunov function ,Stationary distribution ,Stochastic modelling ,General Mathematics ,lcsh:Mathematics ,White noise ,Rumor ,lcsh:QA1-939 ,stationary distribution ,symbols.namesake ,rumor spreading ,symbols ,threshold ,Applied mathematics ,Ergodic theory ,Uniqueness ,Persistence (discontinuity) ,Mathematics - Abstract
In this paper, we develop a rumor spreading model by introducing white noise into the model. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. Finally, we provide some numerical simulations to illustrate the analytical results.
- Published
- 2021
25. On the first general Zagreb eccentricity index
- Author
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Aisha Javed, Muhammad Imran, Muhammad Jamil, and Roslan Hasni
- Subjects
Combinatorics ,eccentricity of vertices ,first general zagreb eccentricity index ,General Mathematics ,extremal graphs ,lcsh:Mathematics ,Shortest path problem ,Bipartite graph ,lcsh:QA1-939 ,Upper and lower bounds ,Graph ,Vertex (geometry) ,Mathematics - Abstract
In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce the first general Zagreb eccentricity index and found upper and lower bounds on this index in terms of order, size and diameter. Moreover, we characterize the extremal graphs in the class of trees, trees with pendant vertices and bipartite graphs. Results on some famous topological indices can be presented as the corollaries of our main results.
- Published
- 2021
26. Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables
- Author
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Rongfang Yan, Bin Lu, and Miaomiao Zhang
- Subjects
Hazard (logic) ,General Mathematics ,lcsh:Mathematics ,Hazard ratio ,Order statistic ,archimedean copula ,Sample (statistics) ,stochastic orders ,lcsh:QA1-939 ,Stochastic ordering ,Statistics ,majorization ,Majorization ,mphr and mprhr models ,Mathematics - Abstract
In this paper, we carry out stochastic comparisons on extreme order statistics (i.e. smallest and largest order statistics) from dependent and heterogeneous samples following modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models. We build the usual stochastic order for sample minimums and maximums, and the hazard rate order on minimums of sample and the reversed hazard rate order on maximums of sample are also derived, respectively. Finally, some examples are given to illustrate the theoretical results.
- Published
- 2021
27. Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system
- Author
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Yunmei Zhao, Huizhang Yang, and Wei Liu
- Subjects
generalized two-component hunter-saxton system ,Pure mathematics ,Conservation law ,Similarity (geometry) ,lie symmetry analysis ,General Mathematics ,Computation ,Infinitesimal ,lcsh:Mathematics ,Mathematics::Analysis of PDEs ,Lie group ,exact solutions ,lcsh:QA1-939 ,Symmetry (physics) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,symmetry reductions ,Lie algebra ,conservation law ,Vector field ,Mathematics - Abstract
Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived. Furthermore, the similarity variables and symmetry reductions of this new generalized two-component Hunter-Saxton system are derived. Under these Lie symmetry reductions, some exact solutions are obtained by using the symbolic computation. Moreover, a conservation law of this system is presented by using the multiplier approach.
- Published
- 2021
28. More on proper nonnegative splittings of rectangular matrices
- Author
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Shu-Xin Miao and Ting Huang
- Subjects
Pure mathematics ,convergence ,General Mathematics ,lcsh:Mathematics ,Comparison results ,rectangular matrix ,lcsh:QA1-939 ,Matrix (mathematics) ,Convergence (routing) ,proper nonnegative splitting ,comparison theorems ,moore-penrose inverse ,Moore–Penrose pseudoinverse ,Mathematics - Abstract
In this paper, we further investigate the single proper nonnegative splittings and double proper nonnegative splittings of rectangular matrices. Two convergence theorems for the single proper nonnegative splitting of a semimonotone matrix are derived, and more comparison results for the spectral radii of matrices arising from the single proper nonnegative splittings and double proper nonnegative splittings of different rectangular matrices are presented. The obtained results generalize the previous ones, and it can be regarded as the useful supplement of the results in [Comput. Math. Appl., 67: 136–144, 2014] and [Results. Math., 71: 93–109, 2017].
- Published
- 2021
29. On the characterization of Pythagorean fuzzy subgroups
- Author
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Supriya Bhunia, Ganesh Ghorai, and Qin Xin
- Subjects
Normal subgroup ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,lcsh:Mathematics ,Pythagorean theorem ,Mathematics::History and Overview ,pythagorean fuzzy coset ,pythagorean fuzzy subgroup ,Intuitionistic fuzzy ,Characterization (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,Algebra ,Physics::Popular Physics ,Mathematics::Group Theory ,pythagorean fuzzy set ,Coset ,Group homomorphism ,pythagorean fuzzy level subgroup ,pythagorean fuzzy normal subgroup ,Mathematics - Abstract
Pythagorean fuzzy environment is the modern tool for handling uncertainty in many decisions making problems. In this paper, we represent the notion of Pythagorean fuzzy subgroup (PFSG) as a generalization of intuitionistic fuzzy subgroup. We investigate various properties of our proposed fuzzy subgroup. Also, we introduce Pythagorean fuzzy coset and Pythagorean fuzzy normal subgroup (PFNSG) with their properties. Further, we define the notion of Pythagorean fuzzy level subgroup and establish related properties of it. Finally, we discuss the effect of group homomorphism on Pythagorean fuzzy subgroup.
- Published
- 2021
30. Finite element approximation of time fractional optimal control problem with integral state constraint
- Author
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Jie Liu and Zhaojie Zhou
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,a priori error estimate ,space time finite element method ,Optimal control ,lcsh:QA1-939 ,integral state constraint ,Finite element method ,Piecewise linear function ,Scheme (mathematics) ,Piecewise ,A priori and a posteriori ,Applied mathematics ,time fractional optimal control problem ,Constant (mathematics) ,Mathematics - Abstract
In this paper we investigate the finite element approximation of time fractional optimal control problem with integral state constraint. A space-time finite element scheme for the control problem is developed with piecewise constant time discretization and piecewise linear spatial discretization for the state equation. A priori error estimate for the space-time discrete scheme is derived. Projected gradient algorithm is used to solve the discrete optimal control problem. Numerical experiments are carried out to illustrate the theoretical findings.
- Published
- 2021
31. A relaxed generalized Newton iteration method for generalized absolute value equations
- Author
-
Senlai Zhu, Yang Cao, and Shi Quan
- Subjects
Generalized Jacobian ,Iterative method ,General Mathematics ,lcsh:Mathematics ,Positive-definite matrix ,globally convergence ,lcsh:QA1-939 ,symbols.namesake ,generalized absolute value equations ,relaxation ,Fixed-point iteration ,Absolute value equation ,symbols ,newton method ,Applied mathematics ,Well-defined ,Coefficient matrix ,Newton's method ,Mathematics - Abstract
To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.
- Published
- 2021
32. Effect of edge and vertex addition on Albertson and Bell indices
- Author
-
Ismail Naci Cangul and Sadik Delen
- Subjects
Vertex (graph theory) ,Vertex deletion ,General Mathematics ,lcsh:Mathematics ,omega invariant ,Topological graph ,vertex addition ,lcsh:QA1-939 ,albertson index ,Graph ,Combinatorics ,bell index ,Computer Science::Discrete Mathematics ,edge addition ,Mathematics ,irregularity index - Abstract
Topological graph indices have been of great interest in the research of several properties of chemical substances as it is possible to obtain these properties only by using mathematical calculations. The irregularity indices are the ones to determine the degree of irregularity of a graph. Albertson and Bell indices are two of them. Edge and vertex deletion and addition are important and useful methods in calculating several properties of a given graph. In this paper, the effects of adding a new edge or a new vertex to a graph on the Albertson and Bell indices are determined.
- Published
- 2021
33. Admissible multivalued hybrid $\mathcal{Z}$-contractions with applications
- Author
-
Monairah Alansari, Mohammed Shehu Shagari, Akbar Azam, and Nawab Hussain
- Subjects
simulation function ,Pure mathematics ,$\mathcal{z}$-contraction ,General Mathematics ,hybrid contraction ,lcsh:Mathematics ,multivalued contraction ,Fixed-point theorem ,Fixed point ,lcsh:QA1-939 ,Nonlinear system ,Matrix (mathematics) ,$b$-metric space ,matrix equation ,fixed point ,Graph (abstract data type) ,Point (geometry) ,Partially ordered set ,Complement (set theory) ,Mathematics - Abstract
In this paper, we introduce new concepts, admissible multivalued hybrid $\mathcal{Z}$-contractions and multivalued hybrid $\mathcal{Z}$-contractions in the framework of $b$-metric spaces and establish sufficient conditions for existence of fixed points for such contractions. A few consequences of our main theorem involving linear and nonlinear contractions are pointed out and discussed by using variants of simulation functions. In the case where our notions are reduced to their single-valued counterparts, the results presented herein complement, unify and generalize a number of significant fixed point theorems due to Branciari, Czerwik, Jachymski, Karapinar and Argawal, Khojasteh, Rhoades, among others. Nontrivial illustrative examples are provided to support the assertions of the obtained results. From application point of view, some fixed point theorems of $b$-metric spaces endowed with partial ordering and graph are deduced and solvability conditions of nonlinear matrix equations are investigated.
- Published
- 2021
34. A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
- Author
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Raúl M. Falcón, Laura Johnson, Stephanie Perkins, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), and Junta de Andalucía
- Subjects
Class (set theory) ,critical set ,Enumeration ,Mathematics::General Mathematics ,General Mathematics ,Order up to ,Structure (category theory) ,enumeration ,Combinatorics ,Set (abstract data type) ,cycle structure ,Latin square ,Mathematics ,Autotopism ,Mathematics::Combinatorics ,Group (mathematics) ,Cycle structure ,lcsh:Mathematics ,Mathematics::History and Overview ,Census ,lcsh:QA1-939 ,autotopism ,latin square ,Critical set - Abstract
This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of the latter, we enumerate all the critical sets based on autotopisms of Latin squares of order up to five. Junta de Andalucía FQM-016
- Published
- 2021
35. eromorphic harmonic univalent functions related with generalized (p,q)-post quantum calculus operators
- Author
-
Shuhai Li, Huo Tang, and Lina Ma
- Subjects
Subordination (linguistics) ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Harmonic (mathematics) ,meromorphic harmonic univalent function ,subordination ,Quantum calculus ,lcsh:QA1-939 ,Convolution ,generalized (p ,Distortion ,convolution ,q)-post quantum calculus operator ,Extreme point ,Mathematics ,Meromorphic function - Abstract
In this paper, we introduce certain subclasses of meromorphic harmonic univalent functions, which are defined by using generalized (p, q)-post quantum calculus operators as well as subordination relationship. Sufficient coefficient conditions, extreme points, distortion bounds and convolution properties for functions belonging to the subclasses are obtained.
- Published
- 2021
36. An averaging principle for stochastic evolution equations with jumps and random time delays
- Author
-
Min Han and Bin Pei
- Subjects
Time delays ,Markov chain ,averaging principle ,General Mathematics ,lcsh:Mathematics ,jumps ,Process (computing) ,Stochastic evolution ,stochastic evolution equations ,lcsh:QA1-939 ,random time delays ,two-time-scale markov switching processes ,Statistical physics ,Limit (mathematics) ,Mathematics - Abstract
This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.
- Published
- 2021
37. A delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response
- Author
-
Anwar Zeb, Ranjit Kumar Upadhyay, A. Pratap, and Yougang Wang
- Subjects
Lyapunov function ,Hopf bifurcation ,delay ,General Mathematics ,Addiction ,media_common.quotation_subject ,lcsh:Mathematics ,Functional response ,periodic solution ,stability ,lcsh:QA1-939 ,Two stages ,Critical point (mathematics) ,Synthetic drugs ,symbols.namesake ,symbols ,Applied mathematics ,synthetic drugs model ,hopf bifurcation ,Bifurcation ,media_common ,Mathematics - Abstract
This paper gropes the stability and Hopf bifurcation of a delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response. The critical point at which a Hopf bifurcation occurs can be figured out by using the escalating time delay of psychologically addicts as a bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are explored with aid of the central manifold theorem and normal form theory. Specially, global stability of the model is proved by constructing a suitable Lyapunov function. To underline effectiveness of the obtained results and analyze influence of some influential parameters on dynamics of the model, some numerical simulations are ultimately addressed.
- Published
- 2021
38. Necessary and sufficient conditions on the Schur convexity of a bivariate mean
- Author
-
Bai-Ni Guo, Hong-Ping Yin, Xi-Min Liu, and Jing-Yu Wang
- Subjects
Mathematics::Combinatorics ,inequality ,General Mathematics ,lcsh:Mathematics ,Regular polygon ,Bivariate analysis ,lcsh:QA1-939 ,Convexity ,Combinatorics ,schur harmonically convex function ,schur convex function ,majorization ,Majorization ,Mathematics::Representation Theory ,bivariate mean ,Mathematics ,Schur-convex function ,necessary and sufficient condition - Abstract
In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.
- Published
- 2021
39. Hermite-Hadamard inequality for new generalized conformable fractional operators
- Author
-
Muhammad Adil Khan and Tahir Ullah Khan
- Subjects
Pure mathematics ,conformable integral ,Inequality ,hermite-hadamard inequality ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,riemann-liouville operators ,Conformable matrix ,lcsh:QA1-939 ,Riemann hypothesis ,symbols.namesake ,Identity (mathematics) ,Section (category theory) ,generalized conformable fractional operators ,Hadamard transform ,Hermite–Hadamard inequality ,symbols ,Mathematics ,media_common - Abstract
This paper is concerned to establish an advanced form of the well-known Hermite-Hadamard (HH) inequality for recently-defined Generalized Conformable (GC) fractional operators. This form of the HH inequality combines various versions (new and old) of this inequality, containing operators of the types Katugampula, Hadamard, Riemann-Liouville, conformable and Riemann, into a single form. Moreover, a novel identity containing the new GC fractional integral operators is proved. By using this identity, a bound for the absolute of the difference between the two rightmost terms in the newly-established Hermite-Hadamard inequality is obtained. Also, some relations of our results with the already existing results are presented. Conclusion and future works are presented in the last section.
- Published
- 2021
40. Stability of general pathogen dynamic models with two types of infectious transmission with immune impairment
- Author
-
B. S. Alofi and S. A. Azoz
- Subjects
Lyapunov function ,pathogen infection ,Steady state (electronics) ,General Mathematics ,lcsh:Mathematics ,cell-to-cell transmission ,lcsh:QA1-939 ,Stability (probability) ,global stability ,Quantitative Biology::Cell Behavior ,symbols.namesake ,immune impairment ,Transmission (telecommunications) ,Exponential stability ,Stability theory ,Bounded function ,symbols ,Applied mathematics ,Quantitative Biology::Populations and Evolution ,Basic reproduction number ,Mathematics - Abstract
In this paper, we investigate the global properties of two general models of pathogen infection with immune deficiency. Both pathogen-to-cell and cell-to-cell transmissions are considered. Latently infected cells are included in the second model. We show that the solutions are nonnegative and bounded. Lyapunov functions are organized to prove the global asymptotic stability for uninfected and infected steady states of the models. Analytical expressions for the basic reproduction number $\mathcal{R}_{0}$ and the necessary condition under which the uninfected and infected steady states are globally asymptotically stable are established. We prove that if $\mathcal{R}_{0}$ < 1 then the uninfected steady state is globally asymptotically stable (GAS), and if $\mathcal{R}_{0}$ > 1 then the infected steady state is GAS. Numerical simulations are performed and used to support the analytical results.
- Published
- 2021
41. On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination
- Author
-
Isnani Darti and Agus Suryanto
- Subjects
Lyapunov function ,Discretization ,Continuous modelling ,General Mathematics ,lcsh:Mathematics ,Finite difference ,dynamically-consistent discretization ,Function (mathematics) ,Nonstandard finite difference scheme ,saturated incidence rate ,local and global stability analysis ,lcsh:QA1-939 ,Euler method ,symbols.namesake ,symbols ,Applied mathematics ,sir epidemic model ,Epidemic model ,lyapunov function ,Mathematics - Abstract
Recently, Hoang and Egbelowo (Boletin de la Sociedad Matematica Mexicana, 2020) proposed a nonstandard finite difference scheme (NSFD) to get a discrete SIR epidemic model with saturated incidence rate and constant vaccination. The discrete model was derived by discretizing the right-hand sides of the system locally and the first order derivative is approximated by the generalized forward difference method but with a restrictive denominator function. Their analysis showed that the NSFD scheme is dynamically-consistent only for relatively small time-step sizes. In this paper, we propose and analyze an alternative NSFD scheme by applying nonlocal approximation and choosing the denominator function such that the proposed scheme preserves the boundedness of solutions. It is verified that the proposed discrete model is dynamically-consistent with the corresponding continuous model for all time-step size. The analytical results have been confirmed by some numerical simulations. We also show numerically that the proposed NSFD scheme is superior to the Euler method and the NSFD method proposed by Hoang and Egbelowo (2020).
- Published
- 2021
42. Determination of three parameters in a time-space fractional diffusion equation
- Author
-
Xiang-Tuan Xiong, Xuemin Xue, and Wanxia Shi
- Subjects
Nonlinear inverse problem ,fractional diffusion equation ,General Mathematics ,lcsh:Mathematics ,uniqueness ,lcsh:QA1-939 ,Regularization (mathematics) ,Tikhonov regularization ,regularization ,Time space ,Boundary data ,Fractional diffusion ,Applied mathematics ,Uniqueness ,Diffusion (business) ,ill-posedness ,Mathematics - Abstract
In this paper, we consider a nonlinear inverse problem of recovering two fractional orders and a diffusion coefficient in a one-dimensional time-space fractional diffusion equation. The uniqueness of fractional orders and the diffusion coefficient, characterizing slow diffusion, can be obtained from the accessible boundary data. Two computational methods, Tikhonov method and Levenberg-Marquardt method, are proposed to solving this problem. Finally, an example is presented to illustrate the efficiency of the two numerical algorithm.
- Published
- 2021
43. The analytical analysis of nonlinear fractional-order dynamical models
- Author
-
Jiabin Xu, Dumitru Baleanu, Rasool Shah, Hassan Khan, Shaban Aly, and A.A. Alderremy
- Subjects
Laplace transform ,General Mathematics ,Homotopy ,lcsh:Mathematics ,Boundary (topology) ,lcsh:QA1-939 ,Fractional calculus ,Nonlinear system ,swift-hohenberg equation ,Bounded function ,caputo operator ,Fluid dynamics ,Applied mathematics ,laplace transform ,adomian decomposition method ,Adomian decomposition method ,Mathematics - Abstract
The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.
- Published
- 2021
44. Input-to-state stability of delayed reaction-diffusion neural networks with multiple impulses
- Author
-
Xiang Xie, Tengda Wei, and Xiaodi Li
- Subjects
Diffusion (acoustics) ,Computer simulation ,Artificial neural network ,General Mathematics ,lcsh:Mathematics ,reaction-diffusion ,State (functional analysis) ,lcsh:QA1-939 ,Stability (probability) ,Term (time) ,input-to-state stability ,delayed neural networks ,Control theory ,Bounded function ,Reaction–diffusion system ,multiple impulses ,Mathematics - Abstract
This paper concerns the input-to-state stability problem of delayed reaction-diffusion neural networks with multiple impulses. After reformulating the neural-network model in term of an abstract impulsive functional differential equation, the criteria of input-to-state stability are established by the direct estimate of mild solution and an integral inequality with infinite distributed delay. It shows that the input-to-state stability of the continuous dynamics can be retained under certain multiple impulsive disturbance and the unstable continuous dynamics can be stabilised by the multiple impulsive control, if the intervals between the multiple impulses are bounded. The numerical simulation of two examples is given to show the effectiveness of theoretical results.
- Published
- 2021
45. Pythagorean fuzzy sets in UP-algebras and approximations
- Author
-
Akarachai Satirad, Aiyared Iampan, and Ronnason Chinram
- Subjects
Approximations of π ,Mathematics::General Mathematics ,General Mathematics ,up-algebra ,pythagorean fuzzy near up-filter ,pythagorean fuzzy up-ideal ,Fuzzy logic ,Physics::Popular Physics ,Mathematics::Algebraic Geometry ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,pythagorean fuzzy up-filter ,pythagorean fuzzy up-subalgebra ,Mathematics ,upper approximation ,lcsh:Mathematics ,Pythagorean theorem ,Mathematics::History and Overview ,lower approximation ,pythagorean fuzzy strong up-ideal ,Lower approximation ,lcsh:QA1-939 ,Algebra ,pythagorean fuzzy set ,ComputingMethodologies_PATTERNRECOGNITION ,Pythagorean fuzzy sets ,ComputingMethodologies_GENERAL ,Upper approximation - Abstract
The aim of this paper is to apply the concept of Pythagorean fuzzy sets to UP-algebras, and then we introduce five types of Pythagorean fuzzy sets in UP-algebras. In addition, we will also discuss the relationship between some assertions of Pythagorean fuzzy sets and Pythagorean fuzzy UP-subalgebras (resp., Pythagorean fuzzy near UP-filters, Pythagorean fuzzy UP-filters, Pythagorean fuzzy UP-ideals, Pythagorean fuzzy strong UP-ideals) in UP-algebras and study upper and lower approximations of Pythagorean fuzzy sets.
- Published
- 2021
46. Fast Crank-Nicolson compact difference scheme for the two-dimensional time-fractional mobile/immobile transport equation
- Author
-
Congcong Li, Lijuan Nong, An Chen, and Qian Yi
- Subjects
fast discrete sine transform ,non-smooth solution ,General Mathematics ,lcsh:Mathematics ,mobile/immobile transport equation ,Order (ring theory) ,lcsh:QA1-939 ,compact difference operator ,Alpha (programming language) ,Operator (computer programming) ,Discrete sine transform ,Scheme (mathematics) ,Applied mathematics ,Crank–Nicolson method ,modified l1 method ,Convection–diffusion equation ,Laplace operator ,Mathematics - Abstract
In this paper, we consider the efficient numerical scheme for solving time-fractional mobile/immobile transport equation. By utilizing the compact difference operator to approximate the Laplacian, we develop an efficient Crank-Nicolson compact difference scheme based on the modified L1 method. It is proved that the proposed scheme is stable with the accuracy of $ O(\tau^{2-\alpha}+h^4) $, where $ \tau $ and $ h $ are respectively the temporal and spatial stepsizes, and the fractional order $ \alpha\in(0, 1) $. In addition, we improve the computational performance for the non-smooth issue by the fast discrete sine transform technology and the method of adding correction terms. Finally, numerical examples are provided to verify the effectiveness of the proposed scheme.
- Published
- 2021
47. Strong Langmuir turbulence dynamics through the trigonometric quintic and exponential B-spline schemes
- Author
-
Mostafa M. A. Khater and A. El-Sayed Ahmed
- Subjects
Computer simulation ,Langmuir Turbulence ,General Mathematics ,B-spline ,lcsh:Mathematics ,the trigonometric quintic (tqbs) and exponential b-spline (ecbs) schemes ,nonlinear klein-gordon-zakharov (kgz) model ,lcsh:QA1-939 ,Quintic function ,Exponential function ,Nonlinear system ,numerical simulation ,Applied mathematics ,Boundary value problem ,Adomian decomposition method ,Mathematics - Abstract
In this manuscript, two recent numerical schemes (the trigonometric quintic and exponential cubic B-spline schemes) are employed for evaluating the approximate solutions of the nonlinear Klein-Gordon-Zakharov model. This model describes the interaction between the Langmuir wave and the ion-acoustic wave in a high-frequency plasma. The initial and boundary conditions are constructed via a novel general computational scheme. [ 1 ] has used five different numerical schemes, such as the Adomian decomposition method, Elkalla-expansion method, three-member of the well-known cubic B-spline schemes. Consequently, the comparison between our solutions and that have been given in [ 1 ], shows the accuracy of seven recent numerical schemes along with the considered model. The obtained numerical solutions are sketched in two dimensional and column distribution to explain the matching between the computational and numerical simulation. The novelty, originality, and accuracy of this research paper are explained by comparing the obtained numerical solutions with the previously obtained solutions.
- Published
- 2021
48. Monotonicity and symmetry of positive solution for 1-Laplace equation
- Author
-
Lin Zhao
- Subjects
Dirichlet problem ,Laplace's equation ,bv space ,General Mathematics ,Operator (physics) ,lcsh:Mathematics ,Mathematical analysis ,1-laplace operator ,Monotonic function ,moving plane method ,lcsh:QA1-939 ,Symmetry (physics) ,Elliptic curve ,Nonlinear system ,symmetry of solutions ,A priori and a posteriori ,mountain pass lemma ,Mathematics - Abstract
In this paper we deal with a Dirichlet problem for an elliptic equation involving the 1-Laplace operator. Under suitable assumptions on the nonlinearity we show that there exists a symmetrical, monotonic and positive solution via the moving plane method. We show the a priori estimates for the positive solution.
- Published
- 2021
49. New generalizations for Gronwall type inequalities involving a ψ-fractional operator and their applications
- Author
-
Jehad Alzabut, Mutti-Ur Rehman, Yassine Adjabi, and Weerawat Sudsutad
- Subjects
generalized gronwall's inequality ,Inequality ,Differential equation ,ulam-hyers stability ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,Stability (learning theory) ,Type (model theory) ,lcsh:QA1-939 ,Fractional operator ,Operator (computer programming) ,Initial value problem ,Applied mathematics ,Uniqueness ,ψ-fractional operators ,ψ-fractional initial value problem ,Mathematics ,media_common ,existence and uniqueness - Abstract
In this paper, we provide new generalizations for the Gronwall's inequality in terms of a $ \psi $-fractional operator. The new forms of Gronwall's inequality are obtained within a general platform that includes several existing results as particular cases. To apply our results and examine their validity, we prove the existence and uniqueness of solutions for $ \psi $-fractional initial value problem. Further, the Ulam-Hyers stability of solutions for $ \psi $-fractional differential equations is discussed. For the sake of illustrating the proposed results, we give some particular examples.
- Published
- 2021
50. Square-mean asymptotically almost periodic solutions of second order nonautonomous stochastic evolution equations
- Author
-
Litao Zhang and Jinghuai Liu
- Subjects
Class (set theory) ,General Mathematics ,lcsh:Mathematics ,Hilbert space ,second order nonautonomous stochastic evolution equations ,Stochastic evolution ,lcsh:QA1-939 ,Square (algebra) ,symbols.namesake ,symbols ,mild solution ,Order (group theory) ,Applied mathematics ,Uniqueness ,square-mean asymptotically almost periodic function ,Mathematics - Abstract
In this paper, we study the existence of square-mean asymptotically almost periodic mild solutions for a class of second order nonautonomous stochastic evolution equations in Hilbert spaces. By using the principle of Banach contractive mapping principle, the existence and uniqueness of square-mean asymptotically almost periodic mild solutions of the equation are obtained. To illustrate the abstract result, a concrete example is given.
- Published
- 2021
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