Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article A Fractional Differential System of Beam Type with Two Generalized Nonlinearities(Palestine Polytechnic University, 2025) Gouari, Yazid; Boulatiour, Yacine; Dahmani, Zoubir; Jarad, FahdArticle Citation - Scopus: 1Study of Impulsive Problem with Caputo Fractional Derivative Involving Nonlocal Conditions Using Fixed Point Theory(Kyungnam University Press, 2025) Dhandapani, Swathi; Umapathi, Karthik Raja; Mathuraiveeran, Jeyaraman; Shah, Kamal; Abdeljawad (Maraaba) T., Thabet; Jarad, Fahd; Abdeljawad, ThabetIn this article, we study the existence of solutions for an impulsive Caupto fractional differential equations with a class of initial value problem dependence on the Lipschitz first derivative conditions. Our main tool is a Banach's fixed point theorem and Leray-Schauder fixed point theorem. We also investigate the existence of fractional Derivative with non-local conditions. An numerical example is given to clarify the results. © 2025 Elsevier B.V., All rights reserved.Article Citation - WoS: 5Citation - Scopus: 6Application of Sumudu and Double Sumudu Transforms To Caputo-Fractional Differential Equations(Eudoxus Press, Llc, 2012) Jarad, Fahd; Jarad, Fahd; Tas, K.; Taş, Kenan; MatematikThe definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems.Article Citation - WoS: 6Citation - Scopus: 8Analytic and Numerical Solutions of Discrete Bagley-Torvik Equation(Springer, 2021) Khashan, M. Motawi; Xavier, Gnanaprakasam Britto Antony; Jarad, Fahd; Meganathan, Murugesan; Abdeljawad, Thabet; Britto Antony Xavier, Gnanaprakasam; Motawi Khashan, M.In this research article, a discrete version of the fractional Bagley-Torvik equation is proposed: del(2)(h)u(t) + A(C)del(nu)(h) u(t) + Bu(t) = f (t), t > 0, (1) where 0 < nu < 1 or 1 < nu < 2, subject to u(0) = a and del(h)u(0) = b, with a and b being real numbers. The solutions are obtained by employing the nabla discrete Laplace transform. These solutions are expressed in terms of Mittag-Leffler functions with three parameters. These solutions are handled numerically for some examples with specific values of some parameters.Article Citation - WoS: 11Citation - Scopus: 11A Generalized Operational Matrix of Mixed Partial Derivative Terms With Applications To Multi-Order Fractional Partial Differential Equations(Elsevier, 2022) Jarad, Fahd; Mirza, Muhammad Umar; Nawaz, Asma; Riaz, Muhammad Bilal; Talib, ImranIn this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap (.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.