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Fractional Calculus and Applied Analysis

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Volume 22, Issue 2

Issues

On fractional differential inclusions with Nonlocal boundary conditions

Charles Castaing / C. Godet-Thobie
  • Université de Bretagne Occidentale Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, 6, avenue Victor Le Gorgeu, CS 9387, F-29238, Brest, Cedex 3, France
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/ Phan D. Phung / Le X. Truong
Published Online: 2019-05-11 | DOI: https://doi.org/10.1515/fca-2019-0027

Abstract

The main purpose of this paper is to study a class of boundary value problem governed by a fractional differential inclusion in a separable Banach space E

Dαu(t)+λDα1u(t)F(t,u(t),Dα1u(t)),t[0,1]I0+βu(t)t=0=0,u(1)=I0+γu(1)

in both Bochner and Pettis settings, where α ∈ ]1, 2], β ∈ [0, 2 – α], λ ≥ 0, γ > 0 are given constants, Dα is the standard Riemann-Liouville fractional derivative, and F : [0, 1] × E × E → 2E is a closed valued multifunction. Topological properties of the solution set are presented. Applications to control problems and subdifferential operators are provided.

MSC 2010: 26A33; 34A60; 34B10; 34A08; 47N70

Key Words and Phrases: fractional differential inclusion; Young measures; Bolza and relaxation problem; subdifferential operators

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About the article

Received: 2017-10-13

Accepted: 2019-02-04

Published Online: 2019-05-11

Published in Print: 2019-04-24


Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 2, Pages 444–478, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0027.

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