Existence and uniqueness of mild solutions for mixed Caputo and Riemann-Liouville semilinear fractional integrodifferential equations with nonlocal conditions

Authors: ASHRAF H. A. RADWAN

Abstract: The purpose of this paper is to investigate the existence and uniqueness of the mild solution to a class of semilinear fractional integrodifferential equations with state-dependent nonlocal fractional conditions. Our problem includes both Caputo and Riemann-Liouville fractional derivatives. Continuous dependence of solutions on initial conditions and $\epsilon$-approximate mild solutions of the considered problem will be discussed.

Keywords: Fractional derivatives, state-dependent nonlocal conditions, continuous dependence, $C_0$-semigroup, $\epsilon$-approximate solutions, fixed points

Full Text: PDF