Abstract. The generalized fractional integral operator and the Caputo type generalized fractional derivative operator are defined which contain the Riemann--Liouville integral operator, the Hadamard fractional integral operator, the Caputo fractional derivative operator and the Caputo type Hadamard fractional derivative operator as special cases. General solutions (the explicit solutions) of the impulsive Caputo type generalized fractional differential equations are given. Applying our results, existence results of solutions of boundary value problems for an impulsive fractional differential equations involved with the Caputo type generalized fractional derivatives are established. Examples and some remarks on recent published papers are presented to illustrate the main theorems.

DOI: 10.14232/actasm-016-793-1

AMS Subject Classification (1991): 34A37, 34K15

Keyword(s): higher order Caputo type generalized fractional differential equation, general solution, impulse effect, Caputo derivative, boundary value problem

Received August 23, 2016. (Registered under 43/2016.)