Approximate controllability of fractional nonlinear differential inclusions

Fractional differential equations have wide applications in both physical and social sciences. This paper addresses the issue of approximate controllability for a class of fractional nonlinear differential inclusions in Banach spaces. A new set of sufficient conditions are formulated and proved for the approximate controllability of fractional nonlinear differential inclusions. In particular, the results are established with the assumption that the associated linear part of system is approximately controllable. Further, the result is extended to obtain the conditions for the solvability of controllability results for fractional inclusions with nonlocal conditions. Finally, an example is presented to illustrate the theory of the obtained result.