A Study of a Non-local Initial Value Problem Fractionally Perturbed

Abstract

In this work, we study a class of fractionally nonlinearly perturbed first order differential equations, subject to a nonlocal initial condition on an unbounded interval, which is the novelty here. By means of the principle of contraction mapping to establish the existence result and by a Gronwall-like inequality, we obtain the asymptotic stability and the λ-stability of the zero solution. Finally, we give an illustrative example.