On sequential fractional Caputo $ (p, q) $-integrodifference equations via three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition

Jarunee Soontharanon; Thanin Sitthiwirattham; Jarunee Soontharanon; Thanin Sitthiwirattham

doi:10.3934/math.2022044

AIMS Mathematics

2022, Volume 7, Issue 1: 704-722. doi: 10.3934/math.2022044

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Research article

On sequential fractional Caputo $ (p, q) $-integrodifference equations via three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition

Jarunee Soontharanon ¹,
Thanin Sitthiwirattham ^{2
,
,}

1.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Received: 09 September 2021 Accepted: 14 October 2021 Published: 15 October 2021
MSC : 39A10, 39A13, 39A70

In this paper, we aim to study the problem of a sequential fractional Caputo $ (p, q) $-integrodifference equation with three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition. We use some properties of $ (p, q) $-integral in this study and employ Banach fixed point theorems and Schauder's fixed point theorems to prove existence results of this problem.
- fractional $ (p, q) $-integral,
- fractional $ (p, q) $-difference,
- three-point boundary value problems,
- existence
Citation: Jarunee Soontharanon, Thanin Sitthiwirattham. On sequential fractional Caputo $ (p, q) $-integrodifference equations via three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition[J]. AIMS Mathematics, 2022, 7(1): 704-722. doi: 10.3934/math.2022044

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Abstract

In this paper, we aim to study the problem of a sequential fractional Caputo $ (p, q) $-integrodifference equation with three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition. We use some properties of $ (p, q) $-integral in this study and employ Banach fixed point theorems and Schauder's fixed point theorems to prove existence results of this problem.

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