Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Abstract

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.