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This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order 3 < u ˆ ≤ 4 and includes a term Θ (β , Z (β)) alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results. [ABSTRACT FROM AUTHOR]

In the early 1940s, P. A. Smith showed that if a finite p-group G acts on a finite dimensional complex X that is mod p acyclic, then its space of fixed points, XG, will also be mod p acyclic. In their recent study of the Balmer spectrum of equivariant stable homotopy theory, Balmer and Sanders were led to study a question that can be shown to be equivalent to the following: if a G-space X is a equivariant homotopy retract of the p-localization of a based finite G-C.W. complex, given H < G and n, what is the smallest r such that if XH is acyclic in the (n+r)th Morava K-theory, then XG must be acyclic in the nth Morava K-theory? Barthel et. al. then answered this when G is abelian, by finding general lower and upper bounds for these "blue shift" numbers which agree in the abelian case. In our paper, we first prove that these potential chromatic versions of Smith's theorem are equiv- alent to chromatic versions of a 1952 theorem of E. E. Floyd, which replaces acyclicity by bounds on dimensions of mod p homology, and thus applies to all finite dimensional G-spaces. This unlocks new techniques and applications in chromatic fixed point theory. Applied to the problem of understanding blue shift numbers, we are able to use classic constructions and representation theory to search for lower bounds. We give a simple new proof of the known lower bound theorem, and then get the first results about nonabelian 2-groups that do not follow from previously known results. In particular, we are able to determine all blue shift numbers for extraspecial 2-groups. Applied in ways analogous to Smith's original applications, we prove new fixed point theorems for K(n)*-homology disks and spheres. Finally, our methods offer a new way of using equivariant results to show the collapsing of certain Atiyah-Hirzebruch spectral sequences in certain cases. Our criterion appears to apply to the calculation of all 2-primary Morava K-theories of all real Grassmanians. [ABSTRACT FROM AUTHOR]

In this article, we discuss the relation theoretic aspects of multivalued weakly contractive mappings to prove fixed point results in the setting of metric spaces endowed with a certain binary relation. Our newly proved results generalize, extend, unify, enrich, sharpen and improve some well-known fixed point theorems of existing literature to the case of multivalued and contractive notion. We also incorporated an example and an application to find the solution of a Volterra-type integral inclusion. [ABSTRACT FROM AUTHOR]

An acute bacterial infection called avian spirochetosis is spread by ticks to a variety of birds. Clinical symptoms can vary greatly and are frequently non-specific. To diagnose a condition, the infectious spirochete must be detected. Here, we structure an epidemic model for the transmission of avian spirochetosis to visualize the interaction between tick and bird populations. The recommended dynamics of avian spirochetosis is illustrated with the help of fractional framework. We inspected the steady-states of the system of the avian spirochetosis for the stability analysis. The next-generation technique is used to evaluate the model's reproduction parameter R 0. The infection-free and endemic steady-state of avian spirochetosis were shown to be locally asymptotically stable under the specified conditions. Through mathematical skills, the positivity of solutions is determined. Additionally, evidence supporting the existence and uniqueness of the avian spirochetosis framework solution has been shown. We conduct modified simulations of the suggested avian spirochetosis system with different input factors to study the complex phenomena of avian spirochetosis under the effect of numerous input parameters. Our outcomes illustrate the significance and plausibility of fractional parameter, and they also suggest that this input parameter may adequately account for these kinds of observations. [ABSTRACT FROM AUTHOR]

This article investigates sufficient conditions for the existence and uniqueness of solutions to the ψ-Hilfer sequential type pantograph fractional boundary value problem. Considering the system depends on a lower-order fractional derivative of an unknown function, the study is carried out in a special working space. Standard fixed point theorems such as the Banach contraction principle and Krasnosel'skii's fixed point theorem are applied to prove the uniqueness and the existence of a solution, respectively. Finally, an example demonstrating our results with numerical simulations is presented. [ABSTRACT FROM AUTHOR]

It has been shown that the findings of d -metric spaces may be deduced from S -metric spaces by considering d ϖ , ϰ = Λ ϖ , ϖ , ϰ . In this study, no such concepts that translate to the outcomes of metric spaces are considered. We establish standard fixed point theorems for integral type contractions involving rational terms in the context of complete S -metric spaces and discuss their implications. We also provide examples to illustrate the work. This paper's findings generalize and expand a number of previously published conclusions. In addition, the abstract conclusions are supported by an application of the Riemann-Liouville calculus to a fractional integral problem and a supportive numerical example. [ABSTRACT FROM AUTHOR]

In this manuscript, we give the generalization of banach's, Kannan's and Chatterjee's fixed Point theorems in neutrosophic metric spaces by using new (TS-IFα) contractive mappings. Also, we establish common fixed point results in neutrosophic metric space by using Occasionally weakly compatible maps for integral type inequalities. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the existence and uniqueness of continuous solutions of the following iterative functional differential equation ... By using of Boyd-Wong's fixed point theorem and under suitable conditions, we establish the existence and uniqueness of a continuous solution. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

Though vaccination protects individuals against many infectious diseases, such protection does not always last forever since a few vaccinated individuals could lose their lifelong immunity and eventually become infected. This study, therefore, determines the effects of imperfect vaccination and memory index on the spread of diseases through the Caputo fractional-order SIRV (Susceptible-Infected-Recovered-Vaccinated) epidemic model. Vital properties of the new model — including the conditions for the existence of a unique solution determined through the fixed-point theory and the conditions for the existence of a positive solution of the model obtained via the Mittag-Leffler function along with the Laplace transformation — are thoroughly studied. Consequently, our simulation results report that an increase in the imperfect vaccination force increases the population of infected individuals. For the memory effect, the higher "memory" the epidemic system has of past states (which corresponds to decreasing values of fractional-order parameter), the greater the peaks and magnitudes of infection shaping the epidemiological system dynamics. [ABSTRACT FROM AUTHOR]

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model's intricate dynamics. [ABSTRACT FROM AUTHOR]

In this manuscript, we discuss fractional fuzzy Goursat problems with Caputo's g H -differentiability. The second-order mixed derivative term in Goursat problems and two types of Caputo's g H -differentiability pose challenges to dealing with Goursat problems. Therefore, in this study, we convert Goursat problems to equivalent systems fuzzy integral equations to deal properly with the mixed derivative term and two types of Caputo's g H -differentiability. In this study, we utilize the concept of metric fixed point theory to discuss the existence of a unique solution of fractional fuzzy Goursat problems. For the useability of established theoretical work, we provide some numerical problems. We also discuss the solutions to numerical problems by conformable double Laplace transform. To show the validity of the solutions we provide 3D plots. We discuss, as an application, why fractional partial fuzzy differential equations are the generalization of usual partial fuzzy differential equations by providing a suitable reason. Moreover, we show the advantages of the proposed fractional transform over the usual Laplace transform. [ABSTRACT FROM AUTHOR]

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations. [ABSTRACT FROM AUTHOR]

In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work. [ABSTRACT FROM AUTHOR]

Fixed point theory is not only essential in mathematics but also to a vast array of applications. In this approach, we provide some fixed point theorems for fuzzy normed space. The triangle property of a fuzzy norm is introduced first. This property is used to demonstrate some fixed point solutions for self-mappings in fuzzy normed space. To demonstrate the importance of the obtained results, an application for the existence of a solution to the ordinary differential equation and the Fredholm integral equation is constructed. [ABSTRACT FROM AUTHOR]

In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete C A T p (0) metric spaces for p ≥ 2 . Our results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlocal fractional coupled system of (k , ψ) -Hilfer fractional differential equations, which involve, in boundary conditions, (k , ψ) -Hilfer fractional derivatives and (k , ψ) -Riemann–Liouville fractional integrals. The existence and uniqueness of solutions are established for the considered coupled system by using standard tools from fixed point theory. More precisely, Banach and Krasnosel'skiĭ's fixed-point theorems are used, along with Leray–Schauder alternative. The obtained results are illustrated by constructed numerical examples. [ABSTRACT FROM AUTHOR]

In an emergency, fear can spread among crowds through one-on-one encounters, with negative societal consequences. The purpose of this research is to create a novel theoretical model of fear (panic) spread in the context of epidemiology during an emergency using the fractal fractional operator. For quantitative analysis, the system's boundedness and positivity are checked. According to the Arzela Ascoli theorem, the model is completely continuous. As a result of the discovery of Schauder's fixed point, it has at least one solution. The existence and uniqueness of the concerned solution have been examined using the fixed point theory technique. Numerical simulations are used to demonstrate the accuracy of the proposed techniques using a generalized form of Mittag-Leffler kernel with a fractal fractional operator. Finally, simulations are utilized to represent the spread of group emotional contagion (spontaneous spread of emotions and related behaviors) dynamically. [ABSTRACT FROM AUTHOR]

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new for isometries of convex sets of Banach spaces as well as for non-locally compact CAT(0)-spaces and injective spaces. Examples of actions on non-proper CAT(0)-spaces come from the study of diffeomorphism groups, birational transformations, and compact Kähler manifolds. A special case of the fixed point theorem provides a novel mean ergodic theorem that in the Hilbert space case implies von Neumann's theorem. The theorem accommodates classically fixed-point-free isometric maps such as those of Kakutani, Edelstein, Alspach and Prus. Moreover, from the main theorem together with some geometric arguments of independent interest, one can deduce that every bounded invertible operator of a Hilbert space admits a nontrivial invariant metric functional on the space of positive operators. This is a result in the direction of the invariant subspace problem although its full meaning is dependent on a future determination of such metric functionals. [ABSTRACT FROM AUTHOR]

This paper proposes a Cahn-Hilliard type inpainting model equipped with a nonlocal diffusion operator. A rigorous analysis of the well-posedness of the stationary solution is established using Schauder's fixed point theory. We construct a time stepping scheme based on the convex splitting method with the nonlocal term treated implicitly and the fidelity term treated explicitly. We prove the consistency, stability and convergence of the semidiscrete-in-time scheme. To the best of our knowledge, this is the first study to present such an analysis for semidiscrete-in-time problems of this model, which provides valuable guidance for parameter selection. Numerical experiments validate the effectiveness of the proposed nonlocal model, which shows superior performance compared to both local and classical total variation models in preserving fine textures and recovering image edges. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of Senapati and Dey on JS-spaces. In this paper, we obtain some coupled fixed point results and support them with some examples. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić's method, which generalizes Banach's theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić's approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić's works while providing valuable insights into this specialized domain. [ABSTRACT FROM AUTHOR]

We set up a unified framework to efficiently compute the shear and bulk viscosities of strongly coupled gauge theories with gravitational holographic duals involving higher derivative corrections. We consider both Weyl4 corrections, encoding the finite 't Hooft coupling corrections of the boundary theory, and Riemann2 corrections, responsible for non-equal central charges c ≠ a of the theory at the ultraviolet fixed point. Our expressions for the viscosities in higher derivative holographic models are extracted from a radially conserved current and depend only on the horizon data. [ABSTRACT FROM AUTHOR]

Improving the control performance of dynamic vibration absorbers has recently been effective by introducing a grounded negative stiffness device. However, the negative stiffness structure is unstable and difficult to achieve in engineering practice , and its major drawback is that it amplif ies the vibration response of the primary system at low frequency region. Meanwhile, some mechanical devices can be combined to make the DVA work even better with a grounded positive stiffness. For this purpose, this paper combines for the first time the control effect of the inerter device and grounded positive stiffness into a three-element DVA model in order to better improve vibration reduction of an undamped primary system under excitation. First, the dynamic equation of motion of the system is written according to Newton 's second law. Then, the steady-state displacement response of the primary system under harmonic excitation is calculated. In order to minimize the resonant response of the primary system around its natural frequency, the extended fixed point theory is applied. Thus, the optimized parameters such as the tuning frequency ratio, the stiffness ratio , and the approximate damping ratio are determined as a function of mass ratio and inerter – mass ratio. From the results analysis, it was found that the inerter – mass ratio has a better working range to guarantee the stability of the coupled system. Then , study on the effect of inerter – mass ratio on the primary system response is carried out. It can be seen that increasing the inerter – mass ratio in the optimal working range can reduce the response of the primary system beyond its uncontrolled static response. However, it is necessary to avoid the situation where the inerter – mass ratio is very large because it can lead to unrealistic optimal parameters. Finally, comparison with other DVA models is show n under harmonic and random excitation of the primary system. It is found that the proposed DVA model in this paper has high control performance and can be used in many engineering practice s. [ABSTRACT FROM AUTHOR]

Invasive‐invaded species problems are of relevance in mathematics applied to population dynamics. In this paper, the mentioned dynamics is introduced based on a fourth‐order parabolic operator, together with coupled non‐linear reaction terms. The fourth‐order operator allows us to model a heterogeneous diffusion, as introduced by the Landau–Ginzburg free energy approach. The reaction terms are given by a coupled non‐linear effect in the invasive species, to account for the action of the invaded species and limited resources, and by a non‐Lipschitz term in the invaded species, to account for possible sprouts, once the invasion occurs. The analysis starts by the proof of existence and uniqueness of solutions, making use of the semi‐group theory and a fixed point argument. Asymptotic solutions to the invasive species are explored with an exponential scaling. Afterward, the problem is analyzed with traveling wave profiles, for which a region of positive solutions is explored. [ABSTRACT FROM AUTHOR]

In fixed point theory, interpolation is acknowledged in numerous areas of research, for instance, earth sciences, metallurgy, surface physics, and so on because of its prospective applications in the estimation of signal sensation analysis. As a result, it is interesting to investigate the fixed point and fixed circle (disc) utilizing interpolative techniques via partial b‐metric spaces in which non‐trivial as well as real generalizations are feasible. We define some improved interpolative contractions to create an environment for the existence of a fixed point and fixed circle and solve a two‐point boundary value problem related to a differential equation of second order. The obtained conclusions are validated by providing illustrative examples. Determining the fixed point of a non‐self mapping, the uniqueness of the fixed point and fixed circle, and the study of fractal interpolants would also be a fascinating investigation in the time to come. [ABSTRACT FROM AUTHOR]

Coronavirus has paralyzed various socio‐economic sectors worldwide. Such unprecedented outbreak was proved to be lethal for about 1,069,513 individuals based upon information released by Worldometers on October 09, 2020. In order to fathom transmission dynamics of the virus, different kinds of mathematical models have recently been proposed in literature. In the continuation, we have formulated a deterministic COVID‐19 model under fractional operators using six nonlinear ordinary differential equations. Using fixed‐point theory and Arzelá Ascoli principle, the proposed model is shown to have existence of unique solution while stability analysis for differential equations involved in the model is carried out via Ulam–Hyers and generalized Ulam–Hyers conditions in a Banach space. Real COVID‐19 cases considered from July 01 to August 14, 2020, in Pakistan were used to validate the model, thereby producing best fitted values for the parameters via nonlinear least‐squares approach while minimizing sum of squared residuals. Elasticity indices for each parameter are computed. Two numerical schemes under singular and non‐singular operators are formulated for the proposed model to obtain various simulations of particularly asymptomatically infectious individuals and of control reproduction number Rc. It has been shown that the fractional operators with order α=9.8254e−01 generated Rc=2.5087 which is smaller than the one obtained under the classical case (α=1). Interesting behavior of the virus is explained under fractional case for the epidemiologically relevant parameters. All results are illustrated from biological viewpoint. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish sufficient conditions for the existence, approximate controllability, and Ulam–Hyers–Rassias stability of solutions for impulsive integrodifferential equations of second order with state-dependent delay using the resolvent operator theory, the approximating technique, Picard operators, and the theory of fixed point with measures of noncompactness. An example is presented to illustrate the efficiency of the result obtained. [ABSTRACT FROM AUTHOR]

The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results. [ABSTRACT FROM AUTHOR]

Recent research indicates the need for improved models of physical phenomena with multiple shocks. One of the newest methods is to use differential inclusions instead of differential equations. In this work, we intend to investigate the existence of solutions for an m-dimensional system of quantum differential inclusions. To ensure the existence of the solution of inclusions, researchers typically rely on the Arzela–Ascoli and Nadler's fixed point theorems. However, we have taken a different approach and utilized the endpoint technique of the fixed point theory to guarantee the solution's existence. This sets us apart from other researchers who have used different methods. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables, and some figures. The paper ends with an example. [ABSTRACT FROM AUTHOR]

This manuscript aims to present new results about the generalized F-contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single and pairs of generalized F-contractions of Hardy–Rogers-type mappings. The established results represent a significant development of numerous previously published findings and results in the existing body of literature. Furthermore, to ensure the practicality and effectiveness of our findings across other fields, we provide an application that demonstrates a unique solution for the semilinear operator system within the Banach space. [ABSTRACT FROM AUTHOR]

The concept referred to as the measure shadowing property for a dynamical system on compact metric space has recently been introduced, acting as an extension of the classical shadowing property by using the property of the Borel measures on the phase space. In this paper, we extend the concept of the measure shadowing property of continuous flows from compact metric spaces to the general metric spaces and demonstrate the equivalence relation between the measure shadowing property and the shadowing property for flows on metric spaces via the shadowable points. [ABSTRACT FROM AUTHOR]

The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established. [ABSTRACT FROM AUTHOR]

This paper focuses on the numerical solutions of a six-compartment fractional model with Caputo derivative. In this model, we obtain non-negative and bounded solutions, equilibrium points, and the basic reproduction number and analyze the stability of disease free equilibrium point. The existence and uniqueness of the solution are proven by employing the Picard–Lindelof approach and fixed point theory. The product–integral trapezoidal rule is employed to simulate the system of FODEs (fractional ordinary differential equations). The numerical results are presented in the form of graphs for each compartment. Finally, the sensitivity of the most important parameter (β) and its impact on COVID-19 dynamics and the basic reproduction number are reported. [ABSTRACT FROM AUTHOR]

The incompressible miscible displacement of two-dimensional Darcy–Forchheimer flow is discussed in this paper, and the mathematical model is formulated by two partial differential equations, a Darcy–Forchheimer flow equation for the pressure and a convection–diffusion equation for the concentration. The model is discretized using a fully mixed virtual element method (VEM), which employs mixed VEMs to solve both the Darcy–Forchheimer flow and concentration equations by introducing an auxiliary flux variable to ensure full mass conservation. By using fixed point theory, we proved the stability, existence and uniqueness of the associated mixed VEM solution under smallness data assumption. Furthermore, we obtain optimal error estimates for concentration and auxiliary flux variables in the |$\texttt {L}^{2}$| - and |$\textbf {L}^{2}$| -norms, as well as for the velocity in the |$\textbf {L}^{2}$| -norm. Finally, several numerical experiments are presented to support the theoretical analysis and to illustrate the applicability for solving actual problems. [ABSTRACT FROM AUTHOR]

In this paper, we study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under some advanced concept of fractional derivative called piecewise fractional-order derivative. Currently, most real-world problems are considered under fractional derivatives because of their stable and global behavior. To deal with and detect the crossover behavior in the dynamics of the proposed model, the piecewise derivative containing the Mittag-Leffler-type kernel combined with classical integer order derivatives in piecewise form is used. First, we will investigate the model for qualitative theory in detail. For qualitative theory, we will use fixed point theory. Additionally, we establish sufficient conditions for Ulam–Hyers (UH) stability. To simulate the model, we develop a numerical algorithm based on the Euler technique. The numerical method is applied to present graphically the approximate solutions of the model. In the final part of the paper, we give a detailed discussion of our numerical results. [ABSTRACT FROM AUTHOR]

The discussion of this paper is to aim to examine application of the notion of C*-algebra valued fuzzy soft metric to homotopy theory using common coupled fixed point results from C*-class functions. We also tried to provide an illustration of our major findings. The results attained expand upon and apply to many of the findings in the literature. [ABSTRACT FROM AUTHOR]

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal–fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal–fractional alcohol addiction model are shown using the Picard–Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam–Hyers coupled with the Ulam–Hyers–Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community. [ABSTRACT FROM AUTHOR]

The hysteretic damping tuned mass damper (HD-TMD), which exhibits linear damping force, has been achieved by variable friction devices. Such devices own the advantages of stable mitigation capacity and easy maintenance compared to viscous damping devices. Previous studies have mainly concentrated on the vibration mitigation effect of the HD-TMD system without explicit consideration of structural acceleration control. In this context, seismic optimizations of HD-TMD for structural acceleration control were presented, and the effective damping of HD-TMD was investigated. H∞ optimizations of the HD-TMD were considered for undamped and lightly damped structures with fixed-point theory, where the closed-form solutions of optimal and improved parameters were derived. Parametric analysis for the dynamic amplification factors (DAFs) of structural acceleration revealed that the closed-form solutions effectively tuned the DAF into double peaks and reduced the maximum response overall frequency. H2 optimizations were conducted with residue theory for the optimization of the undamped structure, and the optimal parameters of HD-TMD subjected to stochastic ground excitation were obtained by numerical searching and curve-fitting techniques. Effective damping of the HD-TMD was consequently examined using the stochastic stationary process in which the damping effect additionally provided to the structure was measured. The effectiveness of the proposed optimal solutions for the HD-TMD in the form of an available engineering variable friction device was thereby corroborated by twenty sets of seismic ground motions. Spectrum's results indicated that the proposed optimal parameters greatly improved the absolute structural acceleration response and provided excellent seismic mitigation capacity for structural displacement response. The response of the equivalent SDOF demonstrated almost the same trend of absolute structural acceleration reduction, which revealed the successful application of effective damping of HD-TMD for designers. Detailed analysis of the earthquake record indicated the functionality and effectiveness of the proposed methods of HD-TMD with the average absolute structural acceleration reduction ratio of 65.86% and 42.66% for maximum reduction and standard deviation reduction, respectively. [ABSTRACT FROM AUTHOR]