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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 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 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 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 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 Fuzzy control problem via random multi-valued equations in symmetric F-n-NLS(MDPI, 2022) Saadati, Reza; Allahviranloo, Tofigh; O'Regan, Donal; Alshammari, Fehaid SalemTo study an uncertain case of a control problem, we consider the symmetric F-n-NLS which is induced by a dynamic norm inspired by a random norm, distribution functions, and fuzzy sets. In this space, we consider a random multi-valued equation containing a parameter and investigate existence, and unbounded continuity of the solution set of it. As an application of our results, we consider a control problem with multi-point boundary conditions and a second order derivative operator.Öğe A novel stability study on volterra integral equations with delay (VIE-D) using the fuzzy minimum optimal controller in matrix-valued fuzzy Banach spaces(Springer Heidelberg, 2023) Eidinejad, Zahra; Saadati, Reza; Allahviranloo, Tofigh; Li, ChenkuanOur main goal in this article is to investigate the Hyers-Ulam-Rassias stability (HURS) for a type of integral equation called Volterra integral equation with delay (VIE-D). First, by considering special functions such as the Wright function (WR), Mittag-Leffler function (ML), Gauss hypergeometric function (GH), H-Fox function (H-F), and also by introducing the aggregation function, we select the best control function by performing numerical calculations to investigate the stability of the desired equation. In the following, using the selected optimal function, i.e., the minimum function, we prove the existence of a unique solution and the HURS of the VI-D equation in the matrix-valued fuzzy space (MVFS) with two different intervals. At the end of each section, we provide a numerical example of the obtained results.Öğe Solving the Fornberg-Whitham Model Derived from Gilson-Pickering Equations by Analytical Methods(Mdpi, 2024) O'Regan, Donal; Aderyani, Safoura Rezaei; Saadati, Reza; Allahviranloo, TofighThis paper focuses on obtaining traveling wave solutions of the Fornberg-Whitham model derived from Gilson-Pickering equations, which describe the prorogation of waves in crystal lattice theory and plasma physics by some analytical techniques, i.e., the exp-function method (EFM), the multi-exp function method (MEFM) and the multi hyperbolic tangent method (MHTM). We analyze and compare them to show that MEFM is the optimum method.
