Approximate controllability of fractional integro-differential equations involving nonlocal initial conditions

Abstract

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.