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

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Authors: M. A. E. HERZALLAH, A. H. A. RADWAN

DOI: 10.46793/KgJMat2106.909H


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 ????-approximate mild solution of the considered problem will be discussed.


Caputo derivative, state dependent nonlocal condition, C0-semigroups, continuous dependence, ????-approximate solution, Krasnoselskii’s fixed point theorem.


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