Darin Brindle, Gaston M. N'Guerekata
Abstract:
This article concerns the existence of mild solutions to the
semilinear fractional differential equation
with nonlocal conditions
where
()
is the Riemann-Liouville derivative,
is a linear densely defined operator of sectorial type
on a complex Banach space
,
is S-asymptotically
-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
-periodic
functions. An application to fractional relaxation-oscillation equations is given.
Submitted August 11, 2019. Published April 7, 2020.
Math Subject Classifications: 34G20, 34G10.
Key Words: S-asymptotically omega-periodic sequence;
fractional semilinear differential equation.
An addendum was posted on April 18, 2020. It corrects Theorem 2.9 and its proof. See the last page of this article.
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Darin Brindle Department of Mathematics Morgan State University Baltimore, MD 21251, USA email: Darin.Brindle@morgan.edu | |
Gaston M. N'Guérékata Department of Mathematics Morgan State University Baltimore, MD 21251, USA email: Gaston.N'Guerekata@morgan.edu |
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