PSEUDO ALMOST AUTOMORPHY OF TWO-TERM FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Zhinan Xia; Jinliang Chai

doi:10.11948/2018.1604

2018 Volume 8 Issue 6

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Zhinan Xia, Jinliang Chai. PSEUDO ALMOST AUTOMORPHY OF TWO-TERM FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1604-1644. doi: 10.11948/2018.1604

Citation:

Zhinan Xia, Jinliang Chai. PSEUDO ALMOST AUTOMORPHY OF TWO-TERM FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1604-1644. doi: 10.11948/2018.1604

PSEUDO ALMOST AUTOMORPHY OF TWO-TERM FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Zhinan Xia¹,
Jinliang Chai²

1 Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, 310023, China;
2 Zhijiang College, Zhejiang University of Technology, Shaoxing, Zhejiang, 312000, China

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Abstract

Abstract

In this paper, by measure theory, we introduce and investigate the concepts of (Stepanov-like) (µ,ν)-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.
- Pseudo almost automorphy /
- fractional functional differential equations /
- Leray-Schauder alternative theorem /
- generalized semigroup theory /
- sectorial operator
MSC: 43A60;34A08;35B40

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References

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