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Fractional Calculus and Applied Analysis

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Volume 18, Issue 1


New Stability Results for Partial Fractional Differential Inclusions with Not Instantaneous Impulses

Saïd Abbas / Mouffak Benchohra
  • Laboratoire de Mathématiques, Université de Sidi Bel-Abbés B. P. 89, 22000, Sidi Bel-Abbés, ALGERIA
  • Department of Mathematics, Faculty of Science King Abdulaziz University P. O. Box 80203, Jeddah 21589, SAUDI ARABIA
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/ Mohamed Abdalla Darwish
  • Department of Mathematics, Sciences Faculty for Girls King Abdulaziz University, Jeddah, SAUDI ARABIA
  • Department of Mathematics, Faculty of Science Damanhour University, Damanhour, EGYPT
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Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0012


In this work, we discuss the existence and Ulam's type stability concepts for a class of partial functional differential inclusions with not instantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is also provided to illustrate our results.

MSC 2010: 26A33; 34A37; 34D10

Key Words and Phrases: fractional differential inclusion; left-sided mixed Riemann-Liouville integral; Caputo fractional order derivative; Darboux problem; fixed point; not instantaneous impulses; Ulam-Hyers-Rassias stability


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About the article

Received: 2014-06-12

Published Online: 2015-02-10

Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 172–191, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0012.

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