Existence and Uniqueness of the Mild Solution of an Abstract Semilinear Fractional Differential Equation with State Dependent Nonlocal Condition

Mohamed A. E. Herzallah, Ashraf H. A. Radwan

The purpose of this paper is to investigate the existence and uniqueness of mild solutions to a semilinear Cauchy problem for an abstract fractional differential equation with state dependent nonlocal condition. Continuous dependence of solutions on initial conditions and local $\epsilon$-approximate mild solution of the considered problem will be discussed.