Composition and convolution theorems for μ-Stepanov pseudo almost periodic functions and applications to fractional integro-differential equations
Date
2018-01-18
Authors
Alvarez, Edgardo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we establish new convulsion and composition theorems for μ-Stepanov pseudo almost periodic functions. We prove that the space of vector-valued μ-Stepanov pseudo almost periodic functions is a Banach space. As an application, we prove the existence and uniqueness of μ-pseudo almost periodic mild solutions for the fractional integro-differential equation.
Dαu(t) = Au(t) + ∫t-∞ α(t - s) Au(s) ds + ƒ(t, u(t)),
where A generates an α-resolvent family {Sα(t)}t ≥ 0 on a Banach space X, α ∈ L1loc (ℝ+), α > 0, the fractional derivative is understood in the sense of Weyl and the nonlinearity ƒ is a μ-Stepanov pseudo almost periodic function.
Description
Keywords
μ-Stepanov pseudo almost periodic, Mild solutions, Fractional integro-differential equations, Composition, Convolution
Citation
Alvarez, E. (2018). Composition and convolution theorems for μ-Stepanov pseudo almost periodic functions and applications to fractional integro-differential equations. <i>Electronic Journal of Differential Equations, 2018</i>(27), pp. 1-15.