SHIFTED LEGENDRE FRACTIONAL PSEUDOSPECTRAL DIFFERENTIATION MATRICES FOR SOLVING FRACTIONAL DIFFERENTIAL PROBLEMS

Mohamed Abdelhakem, Dina Abdelhamied (), Maryam G. Alshehri () and Mamdouh El-Kady
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Mohamed Abdelhakem: Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt2Basic Science Department, School of Engineering, Canadian International College, New Cairo, Egypt
Dina Abdelhamied: Basic Science Department, School of Engineering, Canadian International College “CIC†, Giza, Egypt
Maryam G. Alshehri: Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Mamdouh El-Kady: Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt2Basic Science Department, School of Engineering, Canadian International College, New Cairo, Egypt

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-13

Abstract: A new differentiation technique, fractional pseudospectral shifted Legendre differentiation matrices (FSL D-matrices), was introduced. It depends on shifted Legendre polynomials (SLPs) as a base function. We take into consideration its extreme points and inner product. The technique was used to solve fractional ordinary differential equations (FODEs). Moreover, it extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The novel FSL D-matrices transformed these fractional differential problems (FDPs) into an algebraic system of equations. Also, an error and a convergence analysis for that technique were investigated. Finally, the correctness and efficiency of this technique were examined with test functions and several examples. All the results were compared with the results of other methods to ensure the investigated error analysis.

Keywords: Shifted Legendre Polynomials; Shifted Gauss–Lobatto-Quadrature; Pseudospectral Method; Differential Matrices; Fractional Differential Equation; Fractional Optimal Control; Fractional Integro-Differential Equations; Error Analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400382

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