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Volume 8, Number 6, 2018, Pages 1604-1644                                                                DOI:10.11948/2018.1604
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.
Abstract:
      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.
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