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

Chanisara Metpattarahiran; Thitiporn Linitda; Thanin Sitthiwirattham; Chanisara Metpattarahiran; Thitiporn Linitda; Thanin Sitthiwirattham

doi:10.3934/math.2022829

AIMS Mathematics

2022, Volume 7, Issue 8: 15120-15137. doi: 10.3934/math.2022829

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Research article

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

Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Received: 10 March 2022 Revised: 13 May 2022 Accepted: 07 June 2022 Published: 15 June 2022
MSC : 39A10, 39A13, 39A70

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.
- fractional sum-difference equations,
- boundary value problem,
- existence,
- uniqueness
Citation: Chanisara Metpattarahiran, Thitiporn Linitda, Thanin Sitthiwirattham. Existence results of sequential fractional Caputo sum-difference boundary value problem[J]. AIMS Mathematics, 2022, 7(8): 15120-15137. doi: 10.3934/math.2022829

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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.

References

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