Affiliation:
1. Department of Mathematics, School of Advanced Sciences Vellore Institute of Technology Vellore Tamil Nadu India
2. Department of Mathematics Indian Institute of Technology Roorkee Roorkee Uttarakhand India
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.
Subject
General Engineering,General Mathematics