Browsing by Author "Darzi, Rahmat"

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A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order
(Edp Sciences S A, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Darzi, Rahmat; Agheli, Ahram; 56389
It 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.
An optimal method for approximating the delay differential equations of noninteger order
(Springer Open, 2018) Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389
The 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.
Analysis of the new technique to solution of fractional wave- and heat-like equation
(Jagiellonian Univ Press, 2017) Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389
We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.
Analysis of the new technique to solution of fractional wave- and heat-like equation
(Jagiellonian Univ Press, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389
We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.
Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators
(2020) Baleanu, Dumitru; Darzi, Rahmat; Agheli, Bahram; 56389
A 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.
New study of weakly singular kernel fractional fourth-order partial integro-differential equations based on the optimum q-homotopic analysis method
(Elsevier, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Darzi, Rahmat; Agheli, Bahram; 56389
In 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.
On the Existence and Uniqueness of Solution of A Nonlinear Fractional Differential Equations
(Eudoxus Press, 2013) Baleanu, Dumitru; Mohammadzadeh, B.; Neamaty, Abdolali; Baleanu, Dumitru; 56389
In this paper, we investigate the existence and uniqueness of solution for fractional boundary value problem for nonlinear fractional differential equation D-0+(alpha) u(t) = f(t,u(t)), 0 < t < 1, 2 < alpha <= 3, with the integral boundary conditions {u(0) - gamma(1) u(1) = lambda(1) integral(1)(0) g(1) (s, u(s))ds, u'(0) - gamma(2)u'(1) = lambda(2) integral(1)(0) g(2) (s, u(s))ds, u ''(0) - gamma(2)u ''(1) = 0, where D-0+(alpha) denotes Caputo derivative of order alpha. by using the fixed point theory. We apply the contraction mapping principle and Krasnoselskii's fixed point theorem to obtain some new existence and uniqueness results. Two examples are given to illustrate the main results.