The explicit solution of a class of higher order impulsive fractional differential equation involving Hadamard fractional derivative

Abstract

In this paper, we obtain the explicit solution of a class of singular impulsive fractional differential equation of order [Formula: see text] involving the Hadamard fractional derivatives. In particular, the result is given in the form of necessary and sufficient conditions about the explicit solution. The proof of the main theorem is obtained by converting boundary value problems into integral equations and applying analytical techniques. Finally, some examples explain the application of the main theorem in this paper.

Keywords

• Higher order
• fractional differential equation
• the explicit solution
• Caputo type
• Hadamard fractional derivative