Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates

Numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science, which means increased attention to fractional calculus. This paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a c...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 342; pp. 280 - 294
Main Authors: Al-Smadi, Mohammed, Arqub, Omar Abu
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2019
Subjects:
Caputo fractional derivative
Computational algorithm
Fractional calculus theory
Fredholm operator
Partial integrodifferential equation
Partial integrodifferential equation
Computational algorithm
Fredholm operator
Caputo fractional derivative
Fractional calculus theory
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science, which means increased attention to fractional calculus. This paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a class of partial integrodifferential equations of fractional order in Hilbert space within appropriate kernel functions. The algorithm relies on the reproducing kernel Hilbert space method that provides the solutions in rapidly convergent series representations for the reproducing kernel based upon the Fourier coefficients of orthogonalization process. The Caputo fractional derivatives are introduced to address these issues. Moreover, the error estimate of the generated solutions is established as well as the convergence of the iterative method is investigated under some theoretical assumptions. The superiority and applicability of the present technique is illustrated by handling linear and nonlinear numerical examples. The outcomes obtained are compared with exact solutions and existing methods to confirm the effectiveness of the reproducing kernel method.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.09.020