In this article we establish new convolution and composition theorems for -Stepanov pseudo almost periodic functions. We prove that the space of vector-valued mu-Stepanov pseudo almost periodic functions is a Banach space. As an application, we prove the existence and uniqueness of mu-pseudo almost periodic mild solutions for the fractional integro-differential 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 mu-Stepanov pseudo almost periodic function.
Submitted September 12, 2016. Published January 18, 2018.
Math Subject Classifications: 45D05, 34A12, 45N05.
Key Words: mu-Stepanov pseudo almost periodic; mild solutions,; fractional integro-differential equations; composition; convolution.
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| Edgardo Alvarez |
Universidad del Norte
Departamento de Matemáticas y Estadística
email: firstname.lastname@example.org, email@example.com
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