Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application - Fatemeh Mottaghi; Chenkuan Li; Thabet Abdeljawad; Reza Saadati; Mohammad Bagher Ghaemi (Fractal and Fractional, 2021)
Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear <semantics>ϕ</semantics>-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems.