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Research Article | Open Access

Existence results of sequential fractional Caputo sum-difference boundary value problem

Chanisara Metpattarahiran, Thitiporn Linitda( ), Thanin Sitthiwirattham
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
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Abstract

In this article, we study the existence and uniqueness results for a sequential nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and Schaefer's fixed point theorem. Furthermore, we also show the existence of a positive solution. Our problem contains different orders and four fractional difference operators. Finally, we present an example to display the importance of these results.

Keywords

fractional sum-difference equationsboundary value problemexistenceuniqueness
CLC number: 39A10, 39A13, 39A70

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 15120-15137
DOI: 10.3934/math.2022829

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Cite this article:
Metpattarahiran C, Linitda T, Sitthiwirattham T. Existence results of sequential fractional Caputo sum-difference boundary value problem. AIMS Mathematics, 2022, 7(8): 15120-15137. https://doi.org/10.3934/math.2022829

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Received: 10 March 2022
Revised: 13 May 2022
Accepted: 07 June 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)