Electron. J. Differential Equations,
Vol. 2018 (2018), No. 27, pp. 115.
Composition and convolution theorems for muStepanov pseudo almost periodic
functions and applications to fractional integrodifferential equations
Edgardo Alvarez
Abstract:
In this article we establish new convolution and composition theorems
for
Stepanov pseudo almost periodic functions.
We prove that the space of vectorvalued muStepanov pseudo almost
periodic functions is a Banach space.
As an application, we prove the existence and uniqueness of
mupseudo almost periodic mild solutions for the fractional
integrodifferential equation
where A generates an
resolvent family
on a Banach space X,
,
,
the fractional derivative is understood in the sense of Weyl and the
nonlinearity f is a muStepanov pseudo almost periodic function.
Submitted September 12, 2016. Published January 18, 2018.
Math Subject Classifications: 45D05, 34A12, 45N05.
Key Words: muStepanov pseudo almost periodic; mild solutions,;
fractional integrodifferential equations; composition; convolution.
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Edgardo Alvarez
Universidad del Norte
Departamento de Matemáticas y Estadística
Barranquilla, Colombia
email: edgalp@yahoo.com, ealvareze@uninorte.edu.co

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