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

Poovarasan R; Pushpendra Kumar; Kottakkaran Sooppy Nisar; V. Govindaraj; Poovarasan R; Pushpendra Kumar; Kottakkaran Sooppy Nisar; V. Govindaraj

doi:10.3934/math.2023857

AIMS Mathematics

2023, Volume 8, Issue 7: 16757-16772. doi: 10.3934/math.2023857

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

1.
Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India
2.
Institute for the Future of Knowledge, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
3.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
4.
School of Technology, Woxsen University- Hyderabad-502345, Telangana State, India

Received: 27 March 2023 Revised: 01 May 2023 Accepted: 07 May 2023 Published: 12 May 2023
MSC : 26A33, 65D05, 65D30

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.
- generalized Caputo derivative,
- fractional boundary value problem,
- existence,
- uniqueness, Ulam-Hyers stability
Citation: Poovarasan R, Pushpendra Kumar, Kottakkaran Sooppy Nisar, V. Govindaraj. The existence, uniqueness, and stability analyses of the generalized Caputo-type fractional boundary value problems[J]. AIMS Mathematics, 2023, 8(7): 16757-16772. doi: 10.3934/math.2023857

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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.

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