Mild solutions of conformable fractional differential equations using new generalized conformable fractional derivative and semigroup

Abstract

In this work, we generalize the notion of the conformable derivative. Then, we present the new definition of conformable strongly continuous semigroup and its infinitesimal generator. Further, we study the existence and uniqueness of the mild solution for a conformable differential equation with our
generalized conformable C0-semigroup. Finally, we investigate the continuous dependence between initial data and mild solutions.