Existence and Hyers-Ulam type stability results for nonlinear coupled system of Caputo-Hadamard type fractional differential equations

Subramanian Muthaiah; Dumitru Baleanu; Nandha Gopal Thangaraj; Subramanian Muthaiah; Dumitru Baleanu; Nandha Gopal Thangaraj

doi:10.3934/math.2021012

AIMS Mathematics

2021, Volume 6, Issue 1: 168-194. doi: 10.3934/math.2021012

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Research article

Existence and Hyers-Ulam type stability results for nonlinear coupled system of Caputo-Hadamard type fractional differential equations

1.
Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, India
2.
Department of Mathematics, Cankaya University, Ankara, Turkey
3.
Institute of Space Science, Magurele-Bucharest, Romania
4.
Department of Medical Research, China Medical University, Taichung, Taiwan
5.
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India

Received: 09 May 2020 Accepted: 21 September 2020 Published: 09 October 2020
MSC : 26A33, 34A08, 34B10, 34B15

This paper aims to present the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions. The fractional derivative of the Caputo-Hadamard type is used to formulate the FDEs, and the fractional integrals described in the boundary conditions are due to Hadamard. The consequence of existence is obtained employing the alternative of Leray-Schauder, and Krasnoselskii's, whereas the uniqueness result, is based on the principle of Banach contraction mapping. We examine the stability of the solutions involved in the Hyers-Ulam type. A few examples are presented as an application to illustrate the main results. Finally, it addresses some variants of the problem.
- coupled system,
- Caputo-Hadamard derivatives,
- Hadamard integrals,
- multi-points
Citation: Subramanian Muthaiah, Dumitru Baleanu, Nandha Gopal Thangaraj. Existence and Hyers-Ulam type stability results for nonlinear coupled system of Caputo-Hadamard type fractional differential equations[J]. AIMS Mathematics, 2021, 6(1): 168-194. doi: 10.3934/math.2021012

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Abstract

This paper aims to present the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions. The fractional derivative of the Caputo-Hadamard type is used to formulate the FDEs, and the fractional integrals described in the boundary conditions are due to Hadamard. The consequence of existence is obtained employing the alternative of Leray-Schauder, and Krasnoselskii's, whereas the uniqueness result, is based on the principle of Banach contraction mapping. We examine the stability of the solutions involved in the Hyers-Ulam type. A few examples are presented as an application to illustrate the main results. Finally, it addresses some variants of the problem.

References

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