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This paper aims to derive fractional Grüss type integral inequalities for generalized k-fractional integral operators with Mittag-Leffler function in the kernel. Many new results can be deduced for several integral operators by giving specific values to the parameters involved in Mittag-Leffler function. Moreover, the results of this paper reproduce a lot of already published results.

The main purpose of this work is to discuss the dynamics of a predator-prey dynamical system with Allee effect. The conformable fractional derivative is applied to convert the fractional derivatives which appear in the governing model into ordinary derivatives. We use the piecewise-constant approximation method to discritize the considered model. We also investigate the occurrence of positive equilibrium points. Moreover, we analyse the stability of the equilibrium point using some stability theorems. This work also explores a Neimark-Sacker bifurcation and a period-doubling bifurcation using the theory of bifurcations. The distance between the obtained equilibrium point and some closed curves is examined for various values for the considered bifurcation parameter. The chaos control is nicely analysed using the hybrid control approach. Furthermore, we present the maximum Lyapunov exponents for different values for the bifurcation parameter. Numerical simulations are utilized to ensure that the obtained theoretical results are correct. The used techniques can be applied to deal with predator-prey models in various versions.

We consider a stochastic partial differential equation driven by a Lévy type noise (SPDE). Particular attention is given to the correlation function which measures the moments of the solution. Using the Feynman graph formalism, the solution of the SPDE as well as its truncated moments are given as a sum over specific graphs that are evaluated according to some rules. A remark on some applications will be given at the end of this work.

For the purpose of this research, we give the new concept of essential implicative UPfilter from the concept of essential UP-filters in UP-algebras. Although we know that the concept of implicative UP-filters is UP-filters, we have an example showing that the concept of essential UPfilters does not necessarily be essential implicative UP-filters. After that, we extend the concept of essential implicative UP-filters to t-essential fuzzy implicative UP-filters of UP-algebras and study their relationship based on characteristic functions and upper level subsets.

In this study, we propose a more comprehensive and realistic option pricing model based on approximative fractional Brownian motion, building upon recent advancements in this area. Specifically, we utilize the double 3/2-volatility Jump-Diffusion model, which incorporates approximative fractional Brownian motion with 3/2-volatility, stochastic interest rate, and stochastic intensity. To account for the stochastic interest rate, we employ a two-factor Vasicek model. Notably, our model accommodates negative interest rates. Consequently, we develop a multi-factor model with a stochastic interest rate structure for pricing European options and derive a closed-form pricing formula with an analytical solution by applying some algebraic calculations and Lie symmetries. In order to demonstrate the superiority of our proposed model over other classical approaches, we present numerical results that showcase the value of a European call option. This comparative analysis underscores the advantages of our model in comparison to traditional models.

Frame is a fundamental notion in the study of vector spaces; they offer redundancy and flexibility, which favor their application in various fields of mathematics. This article aims to collect important results of frames in Hibert pro-C∗-modules: Frame, ∗-frame, ∗-K-frame, g-frame, ∗-gframe, ∗-K-g-frame, operator frame, ∗-operator frame, ∗-K-operator frames. We also prove some new notions.

The Shortest Path Problem is a core problem in network optimization, with applications in various scientific and engineering fields, such as communication, transportation, routing, scheduling, and computer networks. Many studies and algorithms have been proposed to solve the traditional shortest path problem, but they often fail to provide optimal solutions when dealing with the uncertainties and vagueness that exist in real-world situations. This study aims to address the Bi-objective Shortest Path Problem using intuitionistic fuzzy arc numbers. The main goal is to find the path that minimizes both cost and time between a given source node and destination node. To handle the complexities introduced by trapezoidal intuitionistic fuzzy numbers, an accuracy function is used. The study suggests a simple yet effective method to solve this problem and shows its efficiency through a numerical example. The research tries to offer innovative solutions for optimizing paths in scenarios where cost and time factors are important, navigating the complex landscape of uncertainty inherent in practical applications.

We obtain symmetries of a family of difference equations and we prove a relationship between these symmetries and similarity variables. We proceed with reduction and eventually derive formula solutions of the difference equations. Furthermore, we discuss the periodic nature of the solutions and analyze the stability of the fixed points. We use Lie point symmetry analysis as our tool in obtaining the solutions. Though we have analyzed a specific family of difference equations in this paper, the algorithmic techniques presented can be utilized to tackle many other difference equations.

Pythagorean fuzzy sets and interval valued Pythagorean fuzzy sets have an important role in decision making techniques. Pythagorean hesitant fuzzy sets are time and again used in dealing with uncertain and vague data. The motive of this paper is to introduce the notion cubic Pythagorean hesitant fuzzy linear spaces. We also present the notion of P(R)-intersection, P(R)-union of cubic Pythagorean hesitant fuzzy linear spaces with examples. Secondly, a series of operators like cubic Pythagorean hesitant fuzzy weighted averaging aggregation operators, cubic Pythagorean hesitant fuzzy order weighted averaging aggregation operators and cubic Pythagorean hesitant fuzzy hybrid order weighted averaging aggregation operators are developed. Then, these aggregation operators are further extended to cubic Pythagorean hesitant fuzzy prioritized weighted averaging aggregation operators by assigning priorities to the criteria. A real life MCDM problem has been illustrated and the effectiveness of the results are compared with those solved using cubic picture hesitant fuzzy prioritized weighted averaging aggregation operators.

The paper investigate a necessary and sufficient condition for the composition operator from harmonic Lipschitz spaces LipHα, (0

We propose a mathematical model for the vibrio cholerae spread under the influence of a seasonal environment with two routes of infection. We proved the existence of a unique bounded positive solution, and that the system admits a global attractor set. The basic reproduction number R0 was calculated for both cases, the fixed and seasonal environment which permits to characterise both, the extinction and the persistence of the disease. We proved that the phage-free equilibrium point is globally asymptotically stable if R0≤1, while the disease will be persist if R0>1. Finally, extensive numerical simulations are given to confirm the theoretical findings.

In this paper, we introduce the notions of minimal u-ω-closed sets, maximal u-ω-open sets, u-ω-paraopen sets, u-ω-paraclosed sets, u-ω-mean open sets and u-ω-mean closed sets in bitopological spaces and obtain several characterizations and some of its properties.

The aim of this paper is to consider a general non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. We apply a two-step technique where approximate solutions of a sequence of a generalized mixed variational inequality problem (GMVIP) are inserted in the iterative method of a selective coordinate-wise decomposition descent method. Its convergence is achieved under coercivity-type assumptions.

In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this property relates to the p.q.-Baer property of R and the existence of a generalized join in I(R) for M-indexed subsets, where I(R) denotes the set of ideals of R. Additionally, we prove a connection between R being a left p.q.-Baer ring and the CM-quasi-Armendariz property. Moreover, we prove that for any element φ2=φ, there exist an idempotent element e2=e such that φ = ce. We then prove that R is quasi-Baer if and only if the crossed product structure R⋊M is quasi-Baer. Finally, we present novel results regarding various constructions for crossed products.

Curves on surfaces and their frames play an important role in differential geometry and in many branches of science such as mechanics and physics. So, we are interested in studying one of these surfaces along a curve lying on a surface. In this paper, we define a surface normal to a surface along a curve lying on a surface in Euclidean 3-space E3. Then, we analyze the necessary and sufficient conditions for that surface to be a ruled surface. Finally, we illustrate the convenience and efficiency of this approach with some representative examples.

Modelling several real-world issues in the fuzzy world extensively uses ordinary differential equations. In this paper, a mechanical vibration system with the given mass, spring constant, damping and external force is modelled as a second-order ordinary differential equation. Due to measurement errors, the initial displacement of the string is approximate and assumed to be a fuzzy number. A fuzzy version of the Sumudu transform procedure is used to figure out this vibrating spring-mass system with fuzzy initial displacement. The output is displayed as a table at various computational stages. The consequences are visibly presented diagrammatically for different values of r and t. There is a good agreement between the computed results and the analytical solution.

In the present research paper, an investigation is undertaken of Steinhaus type theorems for Nörlund-(M, λn) and Nörlund-Euler(M, λn) method of summability in K, a complete non-trivially valued Non-Archimedean field. The conditions for statistical summability for those matrices are discussed in such fields K. The consistency of Nörlund-(M, λn) method of summability is investigated when different sequences are used in the summation process. Further, the relation between Nörlund-Euler(M, λn) summable and its statistical summability is also established.

In this work, we investigate the generalised Hyers-Ulam stability of additive functional inequality in modular spaces with ∆2-conditions and in β-homogeneous Banach spaces.

In this paper, we introduce and develop a new definitions for Katugampola derivative and Katugampola integral. In particular, we defined a (left) fractional derivative starting from a of a function f of order α∈(m-1, m] and a (right) fractional derivative terminating at b, where m ∈ N. Then, we give some proprieties in relation to these operators such as linearity, product rule, quotient rule, power rule, chain rule, and vanishing derivatives for constant functions.

The Double Sadik Transform (DST) represents a generalized double integral transform that has emerged as a highly effective analytical technique for solving numerous scientific problems. This study aims to investigate the DST applied to elementary functions and explore its notable properties, including its duality with the Double Laplace Transform and its capability to transform shifting functions, periodic functions, and convolution functions. Furthermore, the DST methodology is employed to resolve prominent linear fractional Caputo partial differential equations with known solutions commonly encountered in diverse mathematical models. The obtained outcomes are expressed in exact closed form, with the most precise results articulated through the Mittag-Leffler function. These results serve to validate the effectiveness and efficiency of the DST approach, establishing it as a valuable tool for addressing scientific problems involving fractional calculus.

In this manuscript, we suggest a three-step iterative scheme for finding approximate numerical solutions to boundary value problems (BVPs) in a Banach space setting. The underlying strategy of the scheme is based on embedding Green’s function into the three-step M-iterative scheme, which we will call in the paper M-Green’s iterative scheme. We assume certain possible mild conditions to prove the convergence and stability results of the suggested scheme. We also prove numerically that our M-Green iterative scheme is more effective than the corresponding Mann-Green and Khan-Green iterative schemes. Our results improve and extend some recent results in the literature of Green’s function based iteration schemes.

In this paper, we give several characterizations of the Jeribi essential spectrum of a bounded linear operator defined on a Banach space by using the notion of almost weakly compact operators. As a consequence, we prove the stability of the Jeribi essential spectrum under compact perturbations. Furthermore, some characterizations of the Jeribi essential spectra of 3×3 upper triangular block operator matrix are also given.

In this paper, the concepts of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras and (∈, ∈)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are introduced and studied. The UP (BCC)-homomorphic image and inverse image are investigated in (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras. Characterizations of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are discussed.

In the present time world, digital images are crucial for various applications, that includes the medical industry, aircraft and satellite imaging, underwater imaging and so on. For this huge quantities of digital images are produced and used by these applications. For a variety of reasons, these images also need to be transmitted and stored. Therefore, a technique known as compression is applied to resolve this storage issue while transmitting these images. In this article, by extending some unique fixed point theorem results for comparison function on a complete symmetric G-metric space are used and it is a new approach. Moreover, this paper focuses on a compression method using the new structure of extended G-contraction mapping as it assists in compressing the size of the image. Thus, grayscale images are compressed using extended G-contraction mapping. And thus, grayscale images can be represented as matrices in this structure (pixel values). Also, similar images of reduced size can be obtained using an appropriate matrix G-metric and extended G-contraction mapping. The size of the matrix can be substantially reduced without losing any quality by controlling the order of sub matrices. These images are easy to store and transmit, with little variation between the original and contracted image.

In this research paper, the determination of the orientation of a linear interpolation in an interconnected graph can be achieved by measuring its distance from a group of sonar stations strategically positioned within the graph. The study utilizes the metric dimension of toeplitz graphs. Several indices play a crucial role in analyzing motivating activities within such complex structures. The indices covered in this study include the general connectivity index of the toeplitz graph, zagreb indices, symmetric division degree index and randic indices, among others.

The psychological learning theory (PLT) in the formation of moral verdict is represented by the choice-practice paradigm. It involves weighing the effects of various options and choosing one to put into practice. This manuscript is devoted to presenting a general functional equation (FE) for observing animal behavior in such situations. The proposed equation can be used to explain a number of well-known learning and psychological theories. The existence and uniqueness of the solution to a given equation are demonstrated using fixed point (FP) techniques. Furthermore, the stability of the solution to the provided FE is explored in the sense of Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU). Ultimately, to emphasize the importance of our results, two examples are presented.

This paper is concerned with the concepts of upper and lower almost α-*-continuous multifunctions. Moreover, several characterizations of upper and lower almost α-*-continuous multifunctions are investigated. In particular, the relationships between α-*-continuity and almost α-*-continuity are established.

An admissible curve of a pseudo-Galilean space is said to be of constant-ratio if the ratio of the length of the tangent and normal components of its position vector function is a constant. In this paper, we investigate and characterize a spacelike admissible curve of constant-ratio in terms of its curvature functions in the pseudo-Galilean space G13. Also, we study some special curves of constantratio such as T-constant and N-constant types of these curves. Finally, we give some computational examples for constructing the meant curves to demonstrate our theoretical results.

The subject of this paper is a Hoeffding-Azuma type estimation for the difference between an adapted random process and its conditional expectation given a related filtration.

Our main purpose is to introduce the notions of δs(Λ, s)-R0 spaces and δs(Λ, s)-R1 spaces. Moreover, several characterizations of δs(Λ, s)-R0 spaces and δs(Λ, s)-R1 spaces are investigated.

In order to approximate Lebesgue integrable functions on [0, 1], a sequence of linear positive integral operators of Kantorovich type Lσf (x) with a parameter sσ is introduced. The estimates for rates of approximation for functions with a specific smoothness are proved using the appropriate modulus of continuity.

The novelty of the paper is to investigate the nature of conformal Ricci-Yamabe soliton on almost pseudo symmetric, almost pseudo Bochner symmetric, almost pseudo Ricci symmetric and almost pseudo Bochner Ricci symmetric Kähler manifolds. Also, we explore the harmonic aspects of conformal η-Ricci-Yamabe soliton on Kähler spcetime manifolds with a harmonic potential function f and deduce the necessary and sufficient conditions for the 1-form η, which is the g-dual of the vector field ξ on such spacetime to be a solution of Schrödinger-Ricci equation.

This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define open ball, convergence of a sequence and a Cauchy sequence in the context of fuzzy n−controlled metric space. We also prove, by means of an example, that a fuzzy n−controlled metric space is not Hausdorff. At the end of the article, an application is given to prove the uniqueness of the solution to fractional differential equations.

An Almost Boolean Algebra (A, ∧, ∨, 0) (abbreviated as ABA) is an Almost Distributive Lattice (ADL) with a maximal element in which for any x∈A, there exists y∈A such that x∧y = 0 and x∨y is a maximal element in A. If (S, Π, X) is a sheaf of nontrivial discrete ADL’s over a Boolean space such that for any global section f, support of f is open, then it is proved that the set Γ(X, S) of all global sections is an ABA. Conversely, it is proved that every ABA is isomorphic to the ADL of global sections of a suitable sheaf of discrete ADL’s over a Boolean space.

The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value.

In this paper, we introduce and study the concept of vague bi-quasi-interior ideals of Γ-semirings as a generalization of vague bi-ideals, vague quasi-ideals, vague interior ideals, vague bi-quasi-interior ideals, and vague bi-quasi-interior ideals of Γ-semirings.

Developing the probability distributions is increasing extensively over the decades but even though the newly developed distributions have elegant properties and variety of shapes which are applicable in wide areas of real-life situations and a numerous type of data sets. In this article, we introduced a three-parameter positively skewed model named Power Nakagami (PN) distribution based on power transformation. Various statistical properties of the Power Nakagami distribution are derived, including moments. Some reliability measures such as survival function, hazard function, cumulative hazard function and reversed hazard function are discussed also expressions for mills ratio, odd function, elasticity and Lorenz and Bonferroni Curve are developed. Graphical representation of probability density function, cumulative density function and reliability measures are presented. Maximum likelihood estimation is used to estimate the parameters. The distribution is fitted to real life dataset (Tax revenue) to demonstrate the comparison of the new distribution with the base distribution.

The paper is devoted to the study of steady-state transmission problem between two Herschel-Bulkley fluids in a three dimensional thin layer.

The work reported in this article studies the equivalence relationship between fractional integral equation and Ψ-Hilfer Hybrid Langevin Differential Equations of fractional order with nonlocal initial conditions, and then we use this relationship to establish the existence of the results by means of Banach algebra and Schauder’s fixed point theorem. We then demonstrate the uniform local attractiveness of all the solutions.

This paper deals with the concepts of upper and lower weakly α-*-continuous multifunctions. Moreover, some characterizations of upper and lower weakly α-*-continuous multifunctions are investigated. Furthermore, the relationships between almost α-*-continuity and weak α-*-continuity are discussed.

Doubly bordered k-tridiagonal interval linear systems play a crucial role in various mathematical and engineering applications where uncertainty is inherent in the system’s parameters. In this paper, we propose a novel symbolic algorithm for solving such systems efficiently. Our approach combines symbolic computation techniques with interval arithmetic to provide rigorous solutions in the form of tight interval enclosures. By exploiting the tridiagonal structure and employing a divide-and-conquer strategy, our algorithm achieves significantly reduced computational complexity compared to existing numerical methods. We also present theoretical analysis and provide numerical experiments to demonstrate the effectiveness and accuracy of our algorithm. The proposed symbolic algorithm offers a valuable tool for handling doubly bordered k-tridiagonal interval linear systems and opens up possibilities for addressing uncertainty in real-world problems with improved efficiency and reliability.

Cancer is a complex and diverse group of diseases characterized by the uncontrolled growth and spread of abnormal cells in the body. Tumors, which are commonly associated with cancer, refer to abnormal masses of tissue that can develop in various organs or tissues. Cancer can arise from almost any cell type in the body and can affect different organs and systems. The disease occurs when the normal processes of cell division and growth go awry, leading to the formation of malignant tumors. These tumors have the potential to invade nearby tissues and spread to distant parts of the body through a process known as metastasis. In this paper, we aim to present a numerical solution for a recent fractional-order model related to Immune-Chemotherapeutic Treatment for Breast Cancer (ICT) using a novel numerical scheme called the Modified Fractional Euler Method (MFEM). We will also compare our proposed scheme with the traditional numerical scheme, Fractional Euler Method (FEM), through numerical simulations.

We describe the boundedness and compactness of the composition operators Cϕ acting in NK(p,q) on the open unit ball B.

This study aims to investigate the refining relation between two vector general fuzzy automata (VGFA) and prove that refining relation is an equivalence relation. Moreover, Also, we prove that if there exists a refining equivalence between two VGFA, then they have the same language. After that, by considering the notion of refining equivalence, we present the quotient of VGFA. In particular, we show that any quotient of a given VGFA and the VGFA itself have the same language. Furthermore, using the quotient VGFA, we obtain a minimal VGFA with the same language.

The aim of this paper is to introduce the concept of generalized (Λ, α)-closed sets. Moreover, we investigate some characterizations of Λα-T1/2 -spaces, (Λ, α)-normal spaces and (Λ, α)-regular spaces by utilizing generalized (Λ, α)-closed sets.

A device has a better failure rate at specific age t0 property, denoted by BFR-t0 if its failure rate r(t) increases for t≤t0 and for t>t0, r(t) is not less than its value at t0. A test statistic is proposed to test exponentiality versus BFR-t0 based on a randomly right censored sample of size n. Kaplan-Meier estimator is used to estimate the empirical life distribution. Properties of the test are measured by power estimates, estimated risks, and test of normality. The efficiency loss due to censoring is investigated by using tests for censored sample data.

In this paper, we propose a five-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, the short-lived productively infected cells, and the long-lived productively infected cells. The basic reproduction number was established, and the local and global stability of the equilibria of the model were studied. A sensitivity analysis with respect to the model parameters was undertaken. Finally, some numerical simulations are presented to illustrate the theoretical findings.

In this paper, we aim to introduce a new class of open sets namely nigh-open set. Accordingly, we define a topological space called a nigh-topological space. This consequently leads us to outline several new operations in connection with the sets in nigh-topological space coupled with deriving several their properties and relations.

In an almost distributive lattice (ADL), the idea of E-ideals is introduced, and their properties are discussed. In terms of a congruence, an equivalence is established between the minimal prime Eideals of an ADL and its quotient ADL. Finally, topological investigations are performed on prime E-ideals and minimal prime E-ideals.

This paper focuses on the study of Sturm-Liouville eigenvalue problems. In the classical Chebyshev collocation method, the Sturm-Liouville problem is discretized to a generalized eigenvalue problem where the functions represent interpolants in suitably rescaled Chebyshev points. We are concerned with the computation of high-order eigenvalues of Sturm-Liouville problems using an effective method of discretization based on the Chebfun software algorithms with domain truncation. We solve some numerical Sturm-Liouville eigenvalue problems and demonstrate the efficiency of computations.