The new general solution for a class of fractional-order impulsive differential equations involving the Riemann-Liouville type Hadamard fractional derivative

Abstract

In this paper, the new general solution for a class of higher-order impulsive fractional differential equations (IFDEs) involving the Riemann-Liouville (R-L) type Hadamard fractional derivative (FD) is presented. Specifically, the necessary and sufficient conditions of the solution are obtained by converting boundary value problems (BVPs) into integral equations and applying analytical techniques. The results in the paper provide a new method for converting BVPs or initial value problems (IVPs) for IFDEs to integral equations. Finally, some examples are devoted to explaining the application of the theorem.

Keywords

• higher-order fractional differential equation
• general solution
• riemann-liouville type hadamard fractional derivative