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Research Article | Open Access

Stability results for fractional integral pantograph differential equations involving two Caputo operators

Abdelkader Moumen1, Ramsha Shafqat2( ), Zakia Hammouch3, Azmat Ullah Khan Niazi2, Mdi Begum Jeelani1
Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
Department of Sciences, Ecole normale superieure, Moulay Ismail University, Morocco
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 13314, Saudi Arabia
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Abstract

In this paper, we investigate the existence-uniqueness, and Ulam Hyers stability (UHS) of solutions to a fractional-order pantograph differential equation (FOPDE) with two Caputo operators. Banach's fixed point (BFP) and Leray-alternative Schauder's are used to prove the existence- uniqueness of solutions. In addition, we discuss and demonstrate various types of Ulam-stability for our problem. Finally, an example is provided for clarity.

Keywords

fractional derivativefixed pointexistencefractional pantograph equationUlam-Hyers stability
CLC number: 34A07, 34A08, 60G22

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6009-6025
DOI: 10.3934/math.2023303

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Cite this article:
Moumen A, Shafqat R, Hammouch Z, et al. Stability results for fractional integral pantograph differential equations involving two Caputo operators. AIMS Mathematics, 2023, 8(3): 6009-6025. https://doi.org/10.3934/math.2023303

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Received: 26 September 2022
Revised: 09 November 2022
Accepted: 14 November 2022
Published: 15 March 2023
©2023 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)