Browsing by Author "Firoozjaee, M. A."

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Citation - WoS: 66
Citation - Scopus: 76
Numerical Approach of Fokker-Planck Equation With Caputo-Fabrizio Fractional Derivative Using Ritz Approximation
(Elsevier, 2018) Jafari, H.; Lia, A.; Baleanu, D.; Firoozjaee, M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, a type of Fokker-Planck equation (FPE) with Caputo-Fabrizio fractional derivative is considered. We present a numerical approach which is based on the Ritz method with known basis functions to transform this equation into an optimization problem. It leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by solving the algebraic system. The convergence of this technique is discussed extensively. Three examples are included to show the applicability and validity of this method. (C) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 13
Citation - Scopus: 15
On a Numerical Approach To Solve Multi-Order Fractional Differential Equations With Initial/Boundary Conditions
(Asme, 2015) Yousefi, S. A.; Jafari, H.; Baleanu, D.; Firoozjaee, M. A.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, a new method is introduced for solving multi-order fractional differential equations. By transforming the fractional differential equations into an optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation and obtain the coefficients of polynomial expansion. Also, we show the convergence of the method. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.