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Existence Results for Fuzzy Differential Equations with ψ-Hilfer Fractional

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1Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.2Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.3Department of Mathematics, Psg College of Arts and Science, Coimbatore-641014, India.4Department of Mathematics, Faculty of Science,mansoura University, Mansoura 35516, Egypt.

* Corresponding Author: E. M. Elsayed. Email:

Annals of Communications in Mathematics 2022, 5 (1), 38-54. https://doi.org/10.62072/acm.2022.050104

Received: 19 March 2022 |

Accepted: 30 May 2022 |

Published: 30 Jun 2022

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Abstract

This manuscript concerns the fuzzy differential equation involving ψ-Hilfer type fractional derivative with nonlocal condition. By using successive approximation, we obtain the existence, uniqueness results of solution for ψ-Hilfer fuzzy differential equation. Further, nonlocal conditions are extended to the existence results. Furthermore, an application is shown to demonstrate the theoretical conclusions utility.

Keywords

Existence; Fuzzy differential equations; Lipschitz condition; Uniqueness; ψ-Hilfer fractional derivative

Cite This Article

K. Kanagarajan, R. Vivek, D. Vivek, E. M. Elsayed.

Existence Results for Fuzzy Differential Equations with ψ-Hilfer Fractional.

Annals of Communications in Mathematics

2022,

5 (1):

38-54.

https://doi.org/10.62072/acm.2022.050104

Copyright © 2022 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).