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Weighted fractional differential equations with infinite delay in Banach spaces

Qixiang Dong, Can Liu, Zhenbin Fan (2016)

Open Mathematics

This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved,...

Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales

Chao Wang, Yongkun Li (2013)

Annales Polonici Mathematici

We propose a concept of weighted pseudo almost automorphic functions on almost periodic time scales and study some important properties of weighted pseudo almost automorphic functions on almost periodic time scales. As applications, we obtain the conditions for the existence of weighted pseudo almost automorphic mild solutions to a class of semilinear dynamic equations on almost periodic time scales.

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