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Fractional Calculus and Applied Analysis

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Volume 18, Issue 1


Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions

Bashir Ahmad
  • Nonlinear Analysis and Applied Mathematics-Research Group (NAAM) King Abdulaziz University P. O. Box 80203, Jeddah 21589, SAUDI ARABIA
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/ Sotiris K. Ntouyas
Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0017


In this paper, we study nonlocal boundary value problems of fractional differential equations and inclusions with slit-strips integral boundary conditions. We show the existence and uniqueness of solutions for the single valued case (equations) by means of classical contraction mapping principle while the existence result is obtained via a fixed point theorem due to D. O'Regan. The existence of solutions for the multivalued case (inclusions) is established via nonlinear alternative for contractive maps. The results are well illustrated with the aid of examples.

MSC 2010: Primary 34A08; Secondary 34B10; 34A60

Key Words and Phrases: fractional differential equations; fractional differential inclusions; nonlocal boundary value problems; integral boundary conditions; fixed point theorem


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About the article

Received: 2014-08-29

Published Online: 2015-02-10

Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 261–280, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0017.

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