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Öğe a-Whittaker controllability of ?-Hilfer fractional stochastic evolution equations driven by fractional Brownian motion(Springer Heidelberg, 2023) Ghaemi, Mohammad Bagher; Mottaghi, Fatemeh; Saadati, Reza; Allahviranloo, TofighIn this paper, we study the fractional-order system in the sense of?-Hilfer fractional stochastic evolution equations driven by fractional Brownian motion. Applying the fixed point tech-nique, we prove that there exists a mild solution for the problem and introduce a new type of stability. Finally, we present two examples to demonstrate how the obtained results might be applied.Öğe An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing(Elsevier B.V., 2022) Ghalichi, Shabnam Sadat Seyed; Amirfakhrian, Majid; Allahviranloo, TofighSome efficient radial basis functions (RBFs) have a free parameter called the shape parameter that controls the shape of approximating function. This parameter is mainly selected by trial and error related to the problem. Because of the significant role of this value in the accuracy and stability of the RBF method, we propose an algorithm to choose a good value as a shape parameter. In this work, we focus on the interpolating of scattered data approximation and attempt to find a better value of the shape parameter for RBF interpolation. The proposed algorithm selects a good value for the shape parameter by minimizing a cost function which imitates the error between the radial interpolant and the unknown function f that the data points sampled from the function f. The algorithm can be applied to a multidimensional problem of any dimension and for any radial basis function. Also, many experiments including interpolation of one and two dimensional data sets as well as zooming pictures consider investigating the efficiency of this procedure. Also, we show that this algorithm consistently finds a good value for a shape parameter ?.Öğe Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator(AMER INST MATHEMATICAL SCIENCES-AIMS, 2022) Akram, Muhammad; Ihsan, Tayyaba; Allahviranloo, Tofigh; Al-Shamiri, Mohammed M. AliThis study presents a new analytical method to extract the fuzzy solution of the fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential equations (FODEs) using the Laplace operator under the strongly generalized Hukuhara differentiability (SGH-differentiability). To this end, firstly the fourth-order derivative of the fuzzy valued function (FVF) according to the type of the SGH-differentiability is introduced, and then the relationships between the fourth-order derivative of the FVF and its Laplace transform are established. Furthermore, considering the types of differentiabilities and switching points, some fundamental theorems related to the Laplace transform of the fourth-order derivative of the FVF are stated and proved in detail and a method to solve FIVP by the fuzzy Laplace transform is presented in detail. An application of our proposed method in Resistance-Inductance circuit (RL circuit) is presented. Finally, FIVP's solution is graphically analyzed to visualize and support theoretical results.Öğe An analytical study of Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy fourier transform under generalized Hukuhara Caputo fractional differentiability(Springernature, 2024) Akram, Muhammad; Yousuf, Muhammad; Allahviranloo, TofighPythagorean fuzzy fractional calculus provides a strong framework for modeling and analyzing complicated systems with uncertainty and indeterminacy. The primary focus of this article is to investigate the analytical solution of the Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy Fourier transform under generalized Hukuhara Caputo fractional differentiability. To this end, we first establish generalized Hukuhara Caputo fractional differentiability in the context of multivariate Pythagorean fuzzy-valued functions and then we present some results of multivariate Pythagorean generalized Hukuhara Caputo fractional differentiability and generalized Hukuhara integrability. We present the concept of multivariate Pythagorean fuzzy Fourier transform and give some results for Pythagorean fuzzy Fourier transforms of second-order generalized Hukuhara partial differentiability. Finally, we provide a practical application of the Pythagorean fuzzy fractional wave equation to visco-elastic materials including polymers and biological tissues. Their graphs are analyzed to visualize and support the theoretical findings.Öğe An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation(Springer, 2024) Ahadi, Azam; Saadati, Reza; Allahviranloo, Tofigh; O'Regan, DonalTo make better decisions on approximation, we may need to increase reliable and useful information on different aspects of approximation. To enhance information about the quality and certainty of approximating the solution of an Apollonius-type quadratic functional equation, we need to measure both the quality and the certainty of the approximation and the maximum errors. To measure the quality of it, we use fuzzy sets, and to achieve its certainty, we use the probability distribution function. To formulate the above problem, we apply the concept of Z-numbers and introduce a special matrix of the form diag(A,B,C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{diag}(A, B, C)$\end{document} (named the generalized Z-number) where A is a fuzzy time-stamped set, B is the probability distribution function, and C is a degree of reliability of A that is described as a value of A*B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A\ast B$\end{document}. Using generalized Z-numbers, we define a novel control function to investigate H-U-R stability to approximate the solution of an Apollonius-type quadratic functional equation with quality and certainty of the approximation.Öğe Application of fuzzy ABC fractional differential equations in infectious diseases(Univ Tabriz, 2024) Babakordi, Fatemeh; Allahviranloo, TofighIn this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can be used for the system of any equations with unknowns.Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.Öğe Application of the reproducing kernel method for solving linear Volterra integral equations with variable coefficients(Iop Publishing Ltd, 2024) Amoozad, Taher; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen RostamyThis article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.Öğe Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems(Springernature, 2024) Rasekhinezhad, Hajar; Abbasbandy, Saeid; Allahviranloo, Tofigh; Baboliand, EsmailThis paper studies the variable fractional functional boundary value problems (VFF-BVPs) by considering Caputo fractional derivative. We use the reproducing kernel method (RKM) without the orthogonalization process as a smart scheme. For this purpose, we construct a reproducing kernel that does not satisfy the boundary condition of VFF-BVP. With this kernel, we can better approximate the solutions for VFF-BVP. Using this method increases the accuracy of the approximate solution so that a significant error analysis can be produced. Finally, two numerical examples are solved to illustrate the efficiency of the present method.Öğe Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces(SPRINGER HEIDELBERG, 2022) Eidinejad, Zahra; Saadati, Reza; Allahviranloo, TofighIn this paper, considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural networks with mixed delays (NA-CNN-MD). Our main goal is to investigate the existence of a unique solution for the presented system of NA-CNN-MD in the matrix-valued fuzzy spaces and using the fuzzy measure. After investigating the existence of a unique solution of NA-CNNs-MD which are rho-pseudo almost periodically, we prove the Mittag-Leffler stability and Mittag-Leffler attractiveness for rho-pseudo almost periodic functions. Finally, two examples are given to illustrate the theoretical results.Öğe The best approximation of generalized fuzzy numbers based on scaled metric(HINDAWI LTD, 2022) Allahviranloo, Tofigh; Saneifard, Rasoul; Saneifard, Rahim; Kiani, Farzad; Noeiaghdam, Samad; Govindan, VediyappanThe ongoing study has been vehemently allocated to propound an ameliorated alpha-weighted generalized approximation of an arbitrary fuzzy number. This method sets out to lessen the distance between the original fuzzy set and its approximation. In an effort to elaborate the study, formulas are designed for computing the ameliorated approximation by using a multitude of examples. The numerical samples will be exemplified to illuminate the improvement of the nearest triangular approximation (Abbasbandy et al., Triangular approximation of fuzzy numbers using alpha-weighted valuations, Soft Computing, 2019). A variety of features of the ameliorated approximation are then proved.Öğe Bifurcation and multiplicity of solutions of the navier-stokes equations in driven semi-elliptical cavity flow(MDPI, 2022) Ertürk, Ercan; Allahviranloo, TofighIn this paper, bifurcations in the solution of the Navier-Stokes equations are studied and multiple solutions of the driven semi-elliptical cavity flow are presented. The two-dimensional steady incompressible driven viscous flow in a semi-elliptical cavity is solved numerically. To this end, the problem is formulated using an elliptic coordinate system that transforms the geometry conformally and provides a body fitted coordinate system. The presented results show that above a bifurcation Reynolds number the solution of the governing flow equations bifurcates and there exist multiple solutions for a particular Reynolds number when the aspect ratio of the semi-elliptical cavity geometry is 0.26 <= D <= 0.8. The bifurcation Reynolds numbers for different aspect ratios and also multiple solutions at different Reynolds numbers are presented in detail.Öğe Classical and intelligent methods in model extraction and stabilization of a dual-axis reaction wheel pendulum: a comparative study(Elsevier B.V., 2022) Tavakol Aghaei, Vahid; Akbulut, Batuhan Ekin; Tan, Deniz; Allahviranloo, Tofigh; Fernandez Gamiz, Unai; Noeiaghdam, Samad; Bezci, Yüksel EdizControlling underactuated open-loop unstable systems is challenging. In this study, first, both nonlinear and linear models of a dual-axis reaction wheel pendulum (DA-RWP) are extracted by employing Lagrangian equations which are based on energy methods. Then to control the system and stabilize the pendulum's angle in the upright position, fuzzy logic based controllers for both x ? y directions are developed. To show the efficiency of the designed intelligent controller, comparisons are made with its classical optimal control counterparts. In our simulations, as proof of the reliability and robustness of the fuzzy controller, two scenarios including noise-disturbance-free and noisy-disturbed situations are considered. The comparisons made between the classical and fuzzy-based controllers reveal the superiority of the proposed fuzzy logic controller, in terms of time response. The simulation results of our experiments in terms of both mathematical modeling and control can be deployed as a baseline for robotics and aerospace studies as developing walking humanoid robots and satellite attitude systems, respectively.Öğe A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines(Springer Medizin, 2022) Yigit, Gulsemay; Hepson, Ozlem Ersoy; Allahviranloo, TofighThis work proposes a finite element method emphasizing with quartic-trigonometric basis functions for finding the numerical solution of nonlinear Burgers’ equation. The computational scheme is constructed by a discretized space-time hybrid approach using B-spline functions. This methodology produces a system of time-dependent differential equations which is integrated by finite elements technique. The experimental cases including graphical patterns of each wave interaction are simulated by the current computational algorithm. In addition, the method establishes the capacity to provide highly efficient solutions with relative ease of computation. Investigation of the stability analysis shows that the current computational method serves an unconditional stable numerical scheme. © 2022, The Author(s), under exclusive licence to Islamic Azad University.Öğe Conditions to guarantee the existence of solutions for a nonlinear and implicit integro-differential equation with variable coefficients(WILEY, 2022) Li, Chenkuan; Saadati, Reza; Allahviranloo, TofighUsing Babenko's approach, multivariate Mittag-Leffler (MM-L) function, and Krasnoselskii's fixed point theorem, we first investigate the existence of solutions to a Liouville-Caputo nonlinear integro-differential equation with variable coefficients and initial conditions in a Banach space. Then the existence of a positive solution for a variant equation is studied. Finally, we provide examples to illustrate the applications of the main results obtained.Öğe Conflict distance-based variable precision Pythagorean fuzzy rough set in Pythagorean fuzzy decision systems with applications in decision making(Int Scientific Research Publications, 2024) Sahoo, Lakshminarayan; Guchhait, Sanchita; Allahviranloo, Tofigh; Kumar, Jambi Ratna Raja; Tarambale, Manoj Ramesh; Catak, MuammerReal-life decision-making problems are hard to handle by any single uncertainty method because of the complex and uncertain nature of the physical world and the human limitations in understanding it. Therefore, we naturally consider combining the benefits of various uncertainty theories to create a more effective hybrid soft decision-making method. Based on this idea, we use the variable precision rough sets (VPRSs) and Pythagorean fuzzy sets approach to build a new Pythagorean fuzzy rough set (PFRS) model. Since the information system is Pythagorean fuzzy, we use the Pythagorean fuzzy similarity measure to define the new type of distance based on conflict. Then, we merge this notion with the VPRSs to form a variable precision PFRS model and study its properties. We also propose an algorithm for attribute reduction based on this model and apply it to a case study to test its feasibility and performance. The results demonstrate that our model enhances the classification capability of previous models, and it achieves accurate classification by deriving the decision rules.Öğe A discrete heuristic algorithm with swarm and evolutionary features for data replication problem in distributed systems(Springer London Ltd, 2023) Arasteh, Bahman; Allahviranloo, Tofigh; Funes, Peri; Torkamanian-Afshar, Mahsa; Khari, Manju; Catak, MuammerAvailability and accessibility of data objects in a reasonable time is a main issue in distributed systems like cloud computing services. As a result, the reduction of data-related operation times in distributed systems such as data read/write has become a major challenge in the development of these systems. In this regard, replicating the data objects on different servers is one commonly used technique. In general, replica placement plays an essential role in the efficiency of distributed systems and can be implemented statically or dynamically. Estimation of the minimum number of data replicas and the optimal placement of the replicas is an NP-complete optimization problem. Hence, different heuristic algorithms have been proposed for optimal replica placement in distributed systems. Reducing data processing costs as well as the number of replicas, and increasing the reliability of the replica placement algorithms are the main goals of this research. This paper presents a discrete and swarm-evolutionary method using a combination of shuffle-frog leaping and genetic algorithms to data-replica placement problems in distributed systems. The experiments on the standard dataset show that the proposed method reduces data access time by up to 30% with about 14 replicas; whereas the generated replicas by the GA and ACO are, respectively, 24 and 30. The average reduction in data access time by GA and ACO 21% and 18% which shows less efficiency than the SFLA-GA algorithm. Regarding the results, the SFLA-GA converges on the optimal solution before the 10th iteration, which shows the higher performance of the proposed method. Furthermore, the standard deviation among the results obtained by the proposed method on several runs is about 0.029, which is lower than other algorithms. Additionally, the proposed method has a higher success rate than other algorithms in the replica placement problem.Öğe An efficient numerical method for solving m-polar fuzzy initial value problems(Springer Science and Business Media Deutschland GmbH, 2022) Akram, Muhammad; Saqib, Muhammad; Bashir, Shahida; Allahviranloo, TofighSeveral problems in the field of science and technology are modeled with information about the situation that is ambiguous, imprecise, or incomplete. That is, the information about values of parameters, functional relationships, or initial conditions is not given in precise. In these circumstance, existing analytic or numerical methods can be applied only to the selected behavior of the system. For example, by fixing the values of unknown parameters to some credible values. On the basis of partial knowledge, it is impossible to describe the behavior of complete system. Thus, fuzzy differential equations arise in many dynamical models. In modeling of several real-world problems, differential equations frequently involve multi-agent, multi-index, multi-objective, multi-attribute, multi-polar information or uncertainty rather than a single bit. These type of differential equations cannot be well represented by means of fuzzy differential equations or bipolar fuzzy differential equations. Therefore, the theory of m-polar fuzzy sets can be applied to differential equations to handle the problems which have multi-polar information. The aim of this paper is to study differential equation in m-polar fuzzy environment. A fourth-order Runge–Kutta method to solve m-polar FIVPs is presented. The consistency, stability and convergence of suggested method are discussed to ensure its efficiency and validity. Since it requires no higher order function derivatives, the suggested method is straightforward to implement. Euler and Euler modified methods have global truncations errors of O(h) and O(h2) respectively whereas the suggested Runge–Kutta’s global truncation errors of O(h4). Numerical examples are provided to compare the proposed method with Euler and modified Euler methods in terms of global truncation errors (GTE). The numerical findings suggest that the purposed method has an adequate level of accuracy. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.Öğe The exact solutions of the conformable time-fractional modified nonlinear schrodinger equation by the trial equation method and modified trial equation method(Hindawi, 2022) Aderyani, Safoura Rezaei; Saadati, Reza; Vahidi, Javad; Allahviranloo, TofighUsing the trial equation method (TEM) and modified trial equation method (MTEM), firstly, we find the analytical solutions of the conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE), and finally, we present numerical results in tables and charts. © 2022 Safoura Rezaei Aderyani et al.Öğe Existence, uniqueness and matrix-valued fuzzy mittag–leffler–hypergeometric–wright stability for p -hilfer fractional differential equations in matrix-valued fuzzy banach space(Springer Science and Business Media Deutschland GmbH, 2022) Aderyani, Safoura Rezaei; Saadati, Reza; Allahviranloo, TofighWe introduce a new class of fuzzy control functions and define the concept of matrix-valued fuzzy Mittag–Leffler–Hypergeometric–Wright stability. Then, we apply Radu–Mihet method derived from an alternative fixed point theorem to investigate existence, uniqueness and matrix-valued fuzzy Mittag–Leffler–Hypergeometric–Wright stability of a a class of P-Hilfer fractional differential equations in matrix-valued fuzzy Banach space. Next, we show the main results for unbounded domains. An example is given to illustrate the Mittag–Leffler–Hypergeometric–Wright stability for a fractional system. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.Öğe Explicit analytical solutions of an incommensurate system of fractional differential equations in a fuzzy environment(Elsevier Science Inc, 2023) Akram, Muhammad; Muhammad, Ghulam; Allahviranloo, TofighFuzzy fractional models have attracted considerable attention because of their comprehensive and broader understanding of real-world problems. Analytical studies of these models are often complex and difficult. Therefore, it is beneficial to develop a suitable and comprehensive technique to solve these models analytically. In this paper, an explicit analytical technique for solving two-dimensional incommensurate linear fuzzy systems of fractional Caputo differential equations (FLSoCFDEs) considering generalized Hukuhara differentiability (g H-differentiability) is presented and demonstrated. This extracted explicit solution is presented for different classes of such systems, including homogeneous and non-homogeneous cases with commensurate and incommensurate fractional orders. Moreover, the potential solution of FLSoCFDEs in terms of the Mittag-Leffler function involving double series is presented. The originality of the proposed technique is that the fuzzy Cauchy problem is transformed into a system of fuzzy linear Volterra integral equations of second kind and then the solution is extracted using the iterative Picard scheme based on the Banach fixed point theorem. Moreover, several interesting results are derived from FLSoCFDEs in terms of the Mittage-Leffler function for both homogeneous and inhomogeneous cases. To understand the proposed technique, we solve a diffusion process problem (a biological model) and several mass-spring systems as applications. Their graphs are analyzed to illustrate and support the theoretical results.
