Existence of Mild Solution for Impulsive Fractional Differential Equations with Non-local Conditions in Banach Space
Hamdy M. Ahmed *
Higher Institute of Engineering, El-Shorouk Academy, P.O. 3 El-Shorouk City, Cairo, Egypt.
A. A. M. Hassan
Higher Institute of Engineering, El-Shorouk Academy, P.O. 3 El-Shorouk City, Cairo, Egypt.
A. S. Ghanem
Higher Institute of Engineering, El-Shorouk Academy, P.O. 3 El-Shorouk City, Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, by using the probability density function we introduce the mild solution of fractional differential equations with impulsive conditions and obtain various criteria on the existence of mild solutions by using fixed point theorem.
Keywords: Impulsive fractional differential equations, impulsive conditions, mild solution, semigroup theory, probability density function.