Analysis of Fractional Functional Differential Equations of Neutral Type with Nonlocal Conditions

Abstract

This work deals with the existence of solutions for a class of nonlinear nonlocal fractional functional differential equations of neutral type in Banach spaces. In particular, we prove the existence of solutions with the assumptions that the nonlinear parts satisfy locally Lipschitz like conditions and closed linear operator \(-A(t)\) generates analytic semigroup for each \(t \ge 0\). We also investigate global existence of solution and study the continuous dependence of solution on initial data. We conclude the article with an application to the developed results.