Weighted pseudo antiperiodic solutions for fractional integro-differential equations in Banach spaces

Edgardo Alvarez, Carlos Lizama and Rodrigo Ponce

Applied Mathematics and Computation, 2015, vol. 259, issue C, 164-172

Abstract: In this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro-differential equations in the formDαu(t)=Au(t)+∫-∞ta(t-s)Au(s)ds+f(t,u(t)),t∈R,where f(·,u(·)) is Stepanov-like weighted pseudo antiperiodic and A generates a resolvent family of bounded and linear operators on a Banach space X,a∈Lloc1(R+) and α>0. Here the fractional derivative is considered in the sense of Weyl. Also, we give a short proof to show that the vector-valued space of Stepanov-like weighted pseudo antiperiodic functions is a Banach space.

Keywords: Antiperiodic; Weighted; Stepanov; Mild solutions; Banach space; Fractional (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:164-172

DOI: 10.1016/j.amc.2015.02.047

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