Conformable functional evolution equations with nonlocal conditions in Banach spaces

Abstract

In this paper, we study semilinear conformable fractional evolution equations with finite delay subjected to nonlocal initial conditions in an arbitrary Banach space. We prove the existence of mild solutions under compactness type conditions on the nonlinear forcing term. Our result improves and complements several earlier related works. We apply our result to study a functional conformable partial differential equation of transport type.

Keywords

• conformable fractional derivative
• mild solutions
• measure of noncompactness