Please use this identifier to cite or link to this item: http://elar.urfu.ru/handle/10995/118246
Title: A pseudo-spectral scheme for systems of two-point boundary value problems with left and right sided fractional derivatives and related integral equations
Authors: Ameen, I. G.
Elkot, N. A.
Zaky, M. A.
Hendy, A. S.
Doha, E. H.
Issue Date: 2021
Publisher: Tech Science Press
Citation: A pseudo-spectral scheme for systems of two-point boundary value problems with left and right sided fractional derivatives and related integral equations / I. G. Ameen, N. A. Elkot, M. A. Zaky et al. // CMES - Computer Modeling in Engineering and Sciences. — 2021. — Vol. 128. — Iss. 1. — P. 21-41.
Abstract: We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left- and right-sided fractional derivatives. The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations. Then, a Legendre-based spectral collocation method is developed for solving the transformed system. Therefore, we can make good use of the advantages of the Gauss quadrature rule. We present the construction and analysis of the collocation method. These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler-Lagrange equations. Two numerical examples are given to confirm the convergence analysis and robustness of the scheme. © 2021 Tech Science Press. All rights reserved.
Keywords: CONVERGENCE ANALYSIS
SPECTRAL COLLOCATION METHOD
TWO-POINT BOUNDARY VALUE PROBLEMS
WEAKLY SINGULAR INTEGRAL EQUATIONS
BOUNDARY VALUE PROBLEMS
EQUATIONS OF MOTION
NUMERICAL METHODS
OPTIMAL CONTROL SYSTEMS
CONVERGENCE ANALYSIS
EULER-LAGRANGE EQUATIONS
FRACTIONAL DERIVATIVES
FRACTIONAL OPTIMAL CONTROLS
GAUSS QUADRATURE RULES
SPECTRAL COLLOCATION METHOD
TWO POINT BOUNDARY VALUE PROBLEMS
WEAKLY SINGULAR INTEGRAL EQUATIONS
INTEGRAL EQUATIONS
URI: http://elar.urfu.ru/handle/10995/118246
Access: info:eu-repo/semantics/openAccess
RSCI ID: 46854078
SCOPUS ID: 85108971129
WOS ID: 000672695700003
PURE ID: 22823295
ISSN: 15261492
DOI: 10.32604/cmes.2021.015310
metadata.dc.description.sponsorship: Russian Foundation for Basic Research, РФФИ: 19-01-00019
The Russian Foundation for Basic Research (RFBR) Grant No. 19-01-00019.
Appears in Collections:Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

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