Numerical solution of fractional differential equations with temporal two-point BVPs using reproducing kernal Hilbert space method

Yassamine Chellouf; Banan Maayah; Shaher Momani; Ahmad Alawneh; Salam Alnabulsi; Yassamine Chellouf; Banan Maayah; Shaher Momani; Ahmad Alawneh; Salam Alnabulsi

doi:10.3934/math.2021207

AIMS Mathematics

2021, Volume 6, Issue 4: 3465-3485. doi: 10.3934/math.2021207

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Research article

Numerical solution of fractional differential equations with temporal two-point BVPs using reproducing kernal Hilbert space method

1.
Department of Mathematics, Faculty of Science, The university of Jordan, Amman 11942, Jordan
2.
Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

Received: 07 September 2020 Accepted: 17 December 2020 Published: 20 January 2021
MSC : 34A08, 34B15, 46E22, 65R10

In this paper, the reproducing kernel Hilbert space method had been extended to model a numerical solution with two-point temporal boundary conditions for the fractional derivative in the Caputo sense, convergent analysis and error bounds are discussed to verify the theoretical results. Numerical examples are given to illustrate the accuracy and efficiency of the presented approach.
Citation: Yassamine Chellouf, Banan Maayah, Shaher Momani, Ahmad Alawneh, Salam Alnabulsi. Numerical solution of fractional differential equations with temporal two-point BVPs using reproducing kernal Hilbert space method[J]. AIMS Mathematics, 2021, 6(4): 3465-3485. doi: 10.3934/math.2021207

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Abstract

In this paper, the reproducing kernel Hilbert space method had been extended to model a numerical solution with two-point temporal boundary conditions for the fractional derivative in the Caputo sense, convergent analysis and error bounds are discussed to verify the theoretical results. Numerical examples are given to illustrate the accuracy and efficiency of the presented approach.

References

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