Local and global existence of mild solutions for impulsive fractional semilinear integro-differential equation

In this paper, we study the local and global existence of mild solutions for impulsive fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. Also, we review some applications of fractional differential equations.

Research highlights
► We the existence and uniqueness of a mild solution to impulsive semilinear fractional differential equation when the linear part generates a strongly continuous semigroup.
► We also consider the global existence of mild solutions, further assumptions are required for global existence of mild solutions as global existence fails quite frequently.
► We establish the global existence under certain growth conditions of the maps f and g.