Nonlinear Impulsive Fractional Integro Differential Equations
Hamdy M. Ahmed *
Higher Institute of Engineering, El-Shorouk Academy, P.O. 3 El-Shorouk City, Cairo, Egypt.
A. A. M. Hassan
Department of Mathematics, Faculty of Science, Zagazig University, 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
By using xed point theorem we studied the mild solution of fractional integro- differential equations with non-local and impulsive conditions, also we studied the sucient conditions of controllability for this system.
Keywords: Fractional calculus, nonlocal conditions, impulsive conditions, Integro-differential systems, mild solutions, Semigroup theory, probability density function, controllability