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Research Article | Open Access

The existence, uniqueness, and stability analyses of the generalized Caputo-type fractional boundary value problems

Poovarasan R1, Pushpendra Kumar2, Kottakkaran Sooppy Nisar3,4( ), V. Govindaraj1
Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India
Institute for the Future of Knowledge, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
School of Technology, Woxsen University- Hyderabad-502345, Telangana State, India
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Abstract

In this article, we derive some novel results of the existence, uniqueness, and stability of the solution of generalized Caputo-type fractional boundary value problems (FBVPs). The Banach contraction principle, along with necessary features of fixed point theory, is used to establish our results. An example is illustrated to justify the validity of the theoretical observations.

Keywords

generalized Caputo derivativefractional boundary value problemexistenceuniqueness, Ulam-Hyers stability
CLC number: 26A33, 65D05, 65D30

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16757-16772
DOI: 10.3934/math.2023857

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Cite this article:
R P, Kumar P, Nisar KS, et al. The existence, uniqueness, and stability analyses of the generalized Caputo-type fractional boundary value problems. AIMS Mathematics, 2023, 8(7): 16757-16772. https://doi.org/10.3934/math.2023857

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Received: 27 March 2023
Revised: 01 May 2023
Accepted: 07 May 2023
Published: 15 July 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)