Approximate controllability of fractional functional equations with infinite delay

Abstract

Fractional differential equations have been used for constructing many mathematical models in science and engineering. In this paper, we study the approximate controllability results for a class of impulsive fractional differential equations with infinite delay. A new set of sufficient conditions are formulated and proved for achieving the required result. In particular, the results are established under the natural assumptions that the corresponding linear system is approximately controllable. The results are obtained by using the fractional calculus, solution operators and fixed point technique. An example is also provided to illustrate the theory. Further, as a corollary, exact controllability result is discussed without assuming compactness of characteristic solution operators.