The general solution of differential equations with Caputo-Hadamard fractional derivatives and impulsive effect

Abstract

In this paper, the formula of general solution for nonlinear systems with Caputo-Hadamard fractional derivatives and impulsive effect is found by analysis of the limit case (as impulse tends to zero), and it shows that the deviation caused by impulse for the fractional-order nonlinear systems is undetermined. Next, an example is given to illustrate the result.