Existence of the Mild Solutions for Nonlocal Fractional Differential Equations of Sobolev Type with Iterated Deviating Arguments

Abstract

This paper investigates a nonlocal differential equation of Sobolev type of fractional order with iterated deviating arguments in Banach space. The sufficient condition for providing the existence of mild solution to the nonlocal Sobolev-type fractional differential equation with iterated deviating arguments is obtained via technique of fixed-point theorems and analytic semigroup method. Finally, an example is given to explain the applicability of the abstract results developed.