Abstract
We study the existence of weighted -asymptotically -periodic mild solutions for a class of abstract fractional differential equations of the form , where is a linear sectorial operator of negative type.
Highlights
S-asymptotically ω-periodic functions have applications to several problems, for example in the theory of functional differential equations, fractional differential equations, integral equations and partial differential equations
The author has applied the results to partial integrodifferential equations
We study in this paper sufficient conditions for the existence and uniqueness of a weighted S-asymptotically ω-periodic mild solution to the following semi-linear integrodifferential equation of fractional order vt t 0 t Γ
Summary
S-asymptotically ω-periodic functions have applications to several problems, for example in the theory of functional differential equations, fractional differential equations, integral equations and partial differential equations. The concept of S-asymptotic ω-periodicity was introduced in the literature by Henrıquez et al 1, 2. Since it attracted the attention of many researchers see 1–10. The author has established conditions under which a Sv-asymptotically ω-periodic function is asymptotically ω-periodic and discusses the existence of Sv-asymptotically ω-periodic solutions for an integral abstract Cauchy problem. The existence of weighted S-asymptotically ω-periodic mild solutions for integrodifferential equation of fractional order of type 1.1 remains an untreated topic in the literature. To illustrate our main results, we examine sufficient conditions for the existence and uniqueness of a weighted S-asymptotically ω-periodic mild solution to a fractional oscillation equation
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