Browsing by Author "Razzaghi, M."

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Citation - WoS: 37
Citation - Scopus: 33
A Numerical Method Based on the Piecewise Jacobi Functions for Distributed-Order Fractional Schrodinger Equation
(Elsevier, 2023) Heydari, M. H.; Razzaghi, M.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, the distributed-order time fractional version of the Schrodinger problem is defined by replacing the first order derivative in the classical problem with this kind of fractional derivative. The Caputo fractional derivative is employed in defining the used distributed fractional derivative. The orthonormal piecewise Jacobi functions as a novel family of basis functions are defined. A new formulation for the Caputo fractional derivative of these functions is derived. A numerical method based upon these piecewise functions together with the classical Jacobi polynomials and the Gauss- Legendre quadrature rule is constructed to solve the introduced problem. This method converts the mentioned problem into an algebraic problem that can easily be solved. The accuracy of the method is examined numerically by solving some examples.(c) 2022 Elsevier B.V. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 11
Numerical Solution of Distributed-Order Time Fractional Klein-Gordon System
(Elsevier, 2023) Razzaghi, M.; Baleanu, D.; Heydari, M. H.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, the distributed-order time fractional Klein-Gordon-Zakharov system is introduced by substituting the second-order temporal derivative with a distributed-order fractional derivative. The Caputo fractional derivative is utilized to define this kind of distributed-order fractional derivative. A high accuracy approach based on the Chebyshev cardinal polynomials is established for this system. The proposed method turns the fractional system solution into an algebraic system solution by approximating the unknown solution via these cardinal polynomials and engaging their derivative matrices (that are obtained in this paper). Some test problems are considered to investigate the capability and accuracy of this approach.