Journal of Mathematics and Statistics

On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order γ ∈ (0, 1]

Marko Kostić

Journal of Mathematics and Statistics

Abstract

The main aim of this paper is to examine the existence and uniqueness of almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. We deal with the Weyl-Liouville fractional derivatives of order γ ∈ (0, 1], paying special attention to the analysis of semilinear differential inclusions of first order. We use the results from the theory of fractional powers of sectorial multivalued linear operators to achieve our goals, providing an interesting application to semilinear fractional Poisson heat equation in Lp-spaces.

Copyright

© 2017 Marko Kostić. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.