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

Mohammed Al-Smadi and Omar Abu Arqub

Applied Mathematics and Computation, 2019, vol. 342, issue C, 280-294

Abstract: 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.

Keywords: Computational algorithm; Fractional calculus theory; Partial integrodifferential equation; Fredholm operator; Caputo fractional derivative (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (21)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:342:y:2019:i:c:p:280-294

DOI: 10.1016/j.amc.2018.09.020

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