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ArticleOriginal scientific text

Title

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Authors 1, 2, 3

Affiliations

  1. Laboratory of Mathematics, University of Saïda P.O. Box 138, 20000 Saïda, Algeria
  2. Laboratory of Mathematics University Djillali Liabes of Sidi Bel-Abbes P.O. Box 89, 22000, Sidi Bel-Abbes, Algeria
  3. Department of Mathematics Sciences Faculty for Girls, King Abdulaziz University Jeddah, Saudi Arabia

Abstract

In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions

Keywords

ENG
fractional differential inclusion, left-sided mixed Riemann-Liouville integral, Caputo fractional order derivative, upper solution, lower solution, extremal solution, fixed point, Banach algebras, not instantaneous impulses

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2016/36/2
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Pages:
155-179
Main language of publication
English
Received
2016-09-27
Published
2016

DOI: 10.7151/dmdico.1184

Exact and natural sciences