Existence theory and generalized Mittag-Leffler stability for a nonlinear Caputo-Hadamard FIVP via the Lyapunov method-Reference-Cited by-同舟云学术

Existence theory and generalized Mittag-Leffler stability for a nonlinear Caputo-Hadamard FIVP via the Lyapunov method

Published:2022 Issue:8 Volume:7 Page:14419-14433
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Belbali Hadjer¹,Benbachir Maamar²,Etemad Sina³,Park Choonkil⁴,Rezapour Shahram³⁵

Affiliation:

1. Laboratory of Mathematics and Applied Sciences, University of Ghardaia, Algeria

2. Faculty of Sciences, Saad Dahlab University, Blida 1, Algeria

3. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

4. Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Abstract

<abstract><p>This paper discusses the existence, uniqueness and stability of solutions for a nonlinear fractional differential system consisting of a nonlinear Caputo-Hadamard fractional initial value problem (FIVP). By using some properties of the modified Laplace transform, we derive an equivalent Hadamard integral equation with respect to one-parametric and two-parametric Mittag-Leffer functions. The Banach contraction principle is used to give the existence of the corresponding solution and its uniqueness. Then, based on a Lyapunov-like function and a $ \mathcal{K} $-class function, the generalized Mittag-Leffler stability is discussed to solve a nonlinear Caputo-Hadamard FIVP. The findings are validated by giving an example.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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