Title: Cauchy problem on fractional integro-differential evolution equations with infinite delay in fractional power space

Authors: Jie Xin; JinRong Wang

Addresses: School of Mathematics and Information, Ludong University, Yantai 264025, China ' Department of Mathematics, Guizhou University, Guiyang 550025, China

Abstract: In this paper, we study the existence of mild solutions for a class of fractional integro-differential evolution equations with infinite delay in Banach spaces. An appropriate concept for α-mild solutions is introduced. Some existence results for α-mild solutions are investigated. An example is given to illustrate the results.

Keywords: fractional integro-differential evolution equations; infinite delay; mild solutions; analytic compact semigroups; Banach spaces; Cauchy problem.

DOI: 10.1504/IJDSDE.2012.052843

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.4, pp.363 - 378

Available online: 25 Mar 2013 *

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