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

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>

Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals

“…e ⟶ R e are continuous functions and A is real constant. In 2022, Belbali et.al [38] existence theory and generalized Mittag-Leffler stability for a nonlinear Caputo-Hadamard fractional initial value problem using the Lyapunov method. By using main ideas of the aforementioned articles, we investigate the Caputo-Hadamard coupled system of FDEs with the Hadamard fractional integral conditions and present its existence, uniqueness, and Ulam-Hyers stability results.…”