Browsing by Author "Heydari, M. H."

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Citation - WoS: 12
Citation - Scopus: 12
A Computational Approach Based on the Fractional Euler Functions and Chebyshev Cardinal Functions for Distributed-Order Time Fractional 2d Diffusion Equation
(Elsevier, 2023) Heydari, M. H.; Hosseininia, M.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, the distributed-order time fractional diffusion equation is introduced and studied. The Caputo fractional derivative is utilized to define this distributed-order fractional derivative. A hybrid approach based on the fractional Euler functions and 2D Chebyshev cardinal functions is proposed to derive a numerical solution for the problem under consideration. It should be noted that the Chebyshev cardinal functions process many useful properties, such as orthogonal-ity, cardinality and spectral accuracy. To construct the hybrid method, fractional derivative oper-ational matrix of the fractional Euler functions and partial derivatives operational matrices of the 2D Chebyshev cardinal functions are obtained. Using the obtained operational matrices and the Gauss-Legendre quadrature formula as well as the collocation approach, an algebraic system of equations is derived instead of the main problem that can be solved easily. The accuracy of the approach is tested numerically by solving three examples. The reported results confirm that the established hybrid scheme is highly accurate in providing acceptable results.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
An Efficient Method for 3d Helmholtz Equation With Complex Solution
(Amer inst Mathematical Sciences-aims, 2023) Heydari, M. H.; Hosseininia, M.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The Helmholtz equation as an elliptic partial differential equation possesses many applications in the time-harmonic wave propagation phenomena, such as the acoustic cavity and radiation wave. In this paper, we establish a numerical method based on the orthonormal shifted discrete Chebyshev polynomials for finding complex solution of this equation. The presented method transforms the Helmholtz equation into an algebraic system of equations that can be easily solved. Four practical examples are examined to show the accuracy of the proposed technique.
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: 7
Citation - Scopus: 7
A Numerical Method for Distributed-Order Time Fractional 2d Sobolev Equation
(Elsevier, 2023) Heydari, M. H.; Rashid, S.; Jarad, F.; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, the distributed-order time fractional 2D Sobolev equation is introduced. The orthonormal Bernoulli polynomials, as a renowned family of basis functions, are employed to solve this problem. To effectively use of these polynomials in constructing a suitable methodology for this equation, some operational matrices regarding the ordinary and fractional derivative of them are derived. In the developed method, by approximating the unknown solution by means of these polynomials and using the mentioned matrices, as well as applying the collocation technique, a system of algebraic equations (in which the unknowns are the expansion coefficients of the solution function) is obtained, which by solving it, a solution for the main problem is obtained. By providing four test problems, the capability and accuracy of the scheme are studied.
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.