The existence, uniqueness, and stability analyses of the generalized Caputo-type fractional boundary value problems-Reference-Cited by-同舟云学术

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

Published:2023 Issue:7 Volume:8 Page:16757-16772
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

R Poovarasan¹,Kumar Pushpendra²,Nisar Kottakkaran Sooppy³⁴,Govindaraj V.¹

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference26 articles.

1. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.

2. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Elsevier, 1999. https://doi.org/10.1016/s0076-5392(99)9x8001-5

3. M. I. Abbas, Existence results and the Ulam stability for fractional differential equations with hybrid proportional-Caputo derivatives, J. Nonlinear Funct. Anal., 2020 (2020), 1–14. https://doi.org/10.23952/jnfa.2020.48

4. A. Khan, H. Khan, J. F. Gomez-Aguilar, T. Abdeljawad, Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel, Chaos Soliton. Fract., 127 (2019), 422–427. https://doi.org/10.1016/j.chaos.2019.07.026

5. P. Kumar, V. Govindaraj, Z. A. Khan, Some novel mathematical results on the existence and uniqueness of generalized Caputo-type initial value problems with delay, AIMS Mathematics, 7 (2019), 10483–10494. https://doi.org/10.3934/math.2022584

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