Approximate Controllability of Ψ-Hilfer Fractional Neutral Differential Equation with Infinite Delay

Abstract

In this paper, we explain the approximate controllability of Ψ-Hilfer fractional neutral differential equations with infinite delay. The outcome is demonstrated using the infinitesimal operator, fractional calculus, semigroup theory, and the Krasnoselskii’s fixed point theorem. To begin, we emphasise the presence of the mild solution and show that the Ψ-Hilfer fractional system is approximately controllable. Additionally, we present theoretical and practical examples.

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

“…Recently, in [21][22][23] discussed the approximate controllability of fractional stochastic differential systems of order 1 < r < 2. It is possible to support discussions of theory and applications related to controllability by citing the research papers [24][25][26][27][28][29].…”