Existence results for IBVP of $ \left(p, q\right)  $-fractional difference equations in Banach space

Mouataz Billah Mesmouli; Nahed Mustafa Dahshan; Wael W. Mohammed; Mouataz Billah Mesmouli; Nahed Mustafa Dahshan; Wael W. Mohammed

doi:10.3934/math.2024760

AIMS Mathematics

2024, Volume 9, Issue 6: 15748-15760. doi: 10.3934/math.2024760

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Existence results for IBVP of $ \left(p, q\right) $-fractional difference equations in Banach space

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 18 February 2024 Revised: 12 April 2024 Accepted: 24 April 2024 Published: 30 April 2024
MSC : 26A33, 33D05, 34A05, 34A08, 34A12, 34B18, 39A13, 47H10

This article focuses on the problem of integral boundary value for Riemann-Liouville derivatives equipped with $ \left(p, q\right) $-difference calculus in Banach space. To provide further clarification, our focus lies in establishing the existence of a solution to our problem using the measure of noncompactness (m.n.) and the Mönch's fixed point theorem. Our investigation in the Banach space encompasses two nonlinear terms with two distinct orders of derivatives. Our paper concludes with an illustrative example and conclusion.
- boundary value problem,
- existence of solutions,
- Banach space,
- Riemann-Liouville fractional derivatives,
- Mönch fixed point theorem,
- $ \left(p, q\right) $-difference calculus
Citation: Mouataz Billah Mesmouli, Nahed Mustafa Dahshan, Wael W. Mohammed. Existence results for IBVP of $ \left(p, q\right) $-fractional difference equations in Banach space[J]. AIMS Mathematics, 2024, 9(6): 15748-15760. doi: 10.3934/math.2024760

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Abstract

This article focuses on the problem of integral boundary value for Riemann-Liouville derivatives equipped with $ \left(p, q\right) $-difference calculus in Banach space. To provide further clarification, our focus lies in establishing the existence of a solution to our problem using the measure of noncompactness (m.n.) and the Mönch's fixed point theorem. Our investigation in the Banach space encompasses two nonlinear terms with two distinct orders of derivatives. Our paper concludes with an illustrative example and conclusion.

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