Almost Periodic Type Solutions To Fractional Defferential Equations

This paper consists of three parts: the first part introduces the space of almost periodic type functions and the related nature of the gradual expansion; the second part describes the interger-order differential equations of the almost periodic solutions of relevant theories; the last part takes on the existence and uniqueness of almost periodic type solutions of abstract fractional differential equations.Theory of almost periodic function was first proposed by Danish mathematician H. Bohr in 1925-1926, and later was developed by S. Bochner, H. Weyl, A. Besicovitch, and V.V.Stepanov. Fractional calculus includes fractional derivatives and fractional integrals. It means to generalize the differentiation and integration into fractional and complex order. In a related article, the authors Daniela Araya introduced the concept of ? -resolvent families to prove the existence of almost automorphic mild solutions to the following fractional differential equation in the sense of Riemann-Liouville. Later, the author Hui-Sheng relaxed the conditions in literature and obtained the same results.In this paper, we utilize Banach fix-point theorem to get pseudo almost periodic mild solutions and pseudo almost automorphic mild solutions which extends the results in the paper introduced before to a certain extent under appropriate assumptions.