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Pseudo Almost Automorphy of Two-term Fractional Functional Differential Equations
Zhinan Xia,Jinliang Chai
Keywords:Pseudo almost automorphy; Fractional functional differential equations; Leray-Schauder alternative theorem; Generalized semigroup theory; Sectorial operator.
      In this paper, by measure theory, we introduce and investigate the concepts of (Stepanov-like) $(\mu,\nu)$-pseudo almost automorphic of class $r$ and class infinity, respectively. As applications, we establish some sufficient criteria for the existence, uniqueness of pseudo almost automorphic mild solutions to two-term fractional functional differential equations with finite or infinite delay. The working tools are based on the generalization of semigroup theory, Banach contraction mapping principle and Leray-Schauder alternative theorem. Finally, we explore the same topic for a fractional partial functional differential equation with delay.