Existence of mild solutions for perturbed fractional neutral differential equations through deformable derivatives in Banach spaces

Abstract

The deformable derivative [[Formula: see text]] is used in this work to give the necessary restrictions for the existence of mild solutions for perturbed fractional neutral differential equations [PFNDE] in Banach spaces. Several novel existence results are made using fixed point and semigroup techniques. In the end, two numerical examples are given to illustrate the application of the theoretical concepts discussed.