S-asymptotically omega-periodic mild solutions to fractional differential equations
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This article concerns the existence of mild solutions to the semi-linear fractional differential equation
Dαtu(t) = Au(t) + Dα-1t ƒ(t, u(t)), t ≥ 0
with nonlocal conditions u(0) = u0 + g(u) where Dαt(‧) (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+ 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.
CitationBrindle, D., & N'Guérékata, G. M. (2020). S-asymptotically omega-periodic mild solutions to fractional differential equations. Electronic Journal of Differential Equations, 2020(30), pp. 1-12.
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