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Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials
Author(s) -
ElSayed Adel A.,
Agarwal Praveen
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5627
Subject(s) - legendre polynomials , mathematics , variable (mathematics) , algebraic equation , mathematical analysis , collocation method , matrix (chemical analysis) , differential equation , legendre function , numerical analysis , order (exchange) , associated legendre polynomials , ordinary differential equation , classical orthogonal polynomials , gegenbauer polynomials , orthogonal polynomials , nonlinear system , chemistry , physics , finance , quantum mechanics , economics , chromatography
In this paper, shifted Legendre polynomials will be used for constructing the numerical solution for a class of multiterm variable‐order fractional differential equations. In the proposed method, the shifted Legendre operational matrix of the fractional variable‐order derivatives will be investigated. The fundamental problem is reduced to an algebraic system of equations using the constructed matrix and the collocation technique, which can be solved numerically. The error estimate of the proposed method is investigated. Some numerical examples are presented to prove the applicability, generality, and accuracy of the suggested method.