All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
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.
      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.
PDF      Download reader