Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

Abstract

This work studies the controllability of a class of Riemann–Liouville fractional differential equations of order in a new Banach space using fractional cosine family. To derive the existence of solutions, we construct the definition of mild solutions of the system using Laplace transform theory. Then, by assuming the approximate controllability of corresponding linear equation, we prove that the nonlinear dynamical system is approximately controllable using an iterative technique. Lastly, we give an example to illustrate the established theory.