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Research Article | Open Access

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

Mouataz Billah Mesmouli1( )Nahed Mustafa Dahshan2Wael W. Mohammed1,3
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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Abstract

This article focuses on the problem of integral boundary value for Riemann-Liouville derivatives equipped with ( p , q ) -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.

CLC number: 26A33, 33D05, 34A05, 34A08, 34A12, 34B18, 39A13, 47H10

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AIMS Mathematics
Pages 15748-15760

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Cite this article:
Mesmouli MB, Dahshan NM, Mohammed WW. Existence results for IBVP of ( p , q ) -fractional difference equations in Banach space. AIMS Mathematics, 2024, 9(6): 15748-15760. https://doi.org/10.3934/math.2024760

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Received: 18 February 2024
Revised: 12 April 2024
Accepted: 24 April 2024
Published: 30 April 2024
©2024 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)