WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 7Citation - Scopus: 9Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators(Mdpi, 2020) Darzi, Rahmat; Agheli, Bahram; Baleanu, DumitruA new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.Article Citation - WoS: 6Citation - Scopus: 7A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order(Edp Sciences S A, 2018) Darzi, Rahmat; Agheli, Ahram; Baleanu, Dumitru; Agheli, BahramIt is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) D-upsilon y(t) + eta integral(t)(0) (t - s)(zeta-1) y(s) ds = g(t), 1 < upsilon <= 2, 0 < zeta < 1, eta is an element of R, where D-upsilon denotes the Caputo derivative of order upsilon. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.Article Citation - WoS: 17Citation - Scopus: 18New Study of Weakly Singular Kernel Fractional Fourth-Order Partial Integro-Differential Equations Based on the Optimum Q-Homotopic Analysis Method(Elsevier, 2017) Darzi, Rahmat; Agheli, Bahram; Baleanu, DumitruIn this study, the optimum q-homotopic analysis method is employed to solve fourth order partial integro-differential equations with high-order non-integer derivatives. Several specific and clear examples are also given to illustrate the simplicity and capacity of the proposed approach. All of the computations were performed using Mathematica. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 13An Optimal Method for Approximating the Delay Differential Equations of Noninteger Order(Springer, 2018) Agheli, Bahram; Darzi, Rahmat; Baleanu, DumitruThe main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional derivative. This method is preferable to others since it has faster convergence toward homotopy perturbation method, and the convergence rate can be set as a controlled area. Various examples are given to better understand the use of this method. The approximate solutions are compared with exact solutions as well.