Approximate controllability of Ψ‐Caputo fractional differential equation

Abstract

In this paper, we explain how ‐Caputo fractional differential equations are approximately controllable. The outcome is demonstrated using the infinitesimal operator, fractional calculus, semigroup theory, and Krasnoselskii fixed point theorem. To begin, we emphasize the presence of the mild solution and show that the ‐Caputo fractional system is approximately controllable. Additionally, an example is provided to illustrate the idea.