S-asymptotically omega-periodic mild solutions to fractional differential equations

Date

2020-04-07

Authors

Brindle, Darin
N'Guerekata, Gaston

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the existence of mild solutions to the semi-linear fractional differential equation <pre>D<sup>α</sup><sub>t</sub>u(t) = Au(t) + D<sup>α-1</sup><sub>t</sub> ƒ(t, u(t)), t ≥ 0</pre> <p>with nonlocal conditions u(0) = u<sub>0</sub> + g(u) where D<sup>α</sup><sub>t</sub>(‧) (1 < α < 2) is the Riemann-Liouville derivative, A : D(A) ⊂ X → X is a linear densely defined operator of sectorial type on a complex Banach space X, ƒ : ℝ<sup>+</sup> x X → X is S-asymptotically ω-periodic with respect to the first variable. We use the Krsnoselskii's theorem to prove our main theorem. The results obtained are new even in the context of asymptotically ω-periodic functions. An application to fractional relaxation-oscillation equations is given.

Description

Keywords

S-asymptotically omega-periodic sequence, Fractional semilinear differential equation

Citation

Brindle, D., & N'Guérékata, G. M. (2020). S-asymptotically omega-periodic mild solutions to fractional differential equations. <i>Electronic Journal of Differential Equations, 2020</i>(30), pp. 1-12.

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Attribution 4.0 International

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