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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

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

Marko Kostić1
  • 1 University of Novi Sad, Serbia

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.

Journal of Mathematics and Statistics
Volume 13 No. 3, 2017, 240-250

DOI: https://doi.org/10.3844/jmssp.2017.240.250

Submitted On: 18 May 2017 Published On: 26 July 2017

How to Cite: Kostić, M. (2017). On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order γ ∈ (0, 1]. Journal of Mathematics and Statistics, 13(3), 240-250. https://doi.org/10.3844/jmssp.2017.240.250

Open AccessCopyright: © 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.

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Keywords

  • Weyl-Liouville Fractional Derivatives
  • Almost Periodicity
  • Stepanov Almost Periodicity
  • Multivalued Linear Operators
  • Fractional Powers of Operators
  • 2010 Mathematics Subject Classification, Primary 34A60, 47D06; Secondary 47D03, 47D99