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The European Physical Journal Special Topics

, Volume 226, Issue 16–18, pp 3355–3368 | Cite as

Lyapunov-type inequalities for fractional difference operators with discrete Mittag-Leffler kernel of order 2 < α < 5/2

  • Thabet Abdeljawad
  • Fadila Madjidi
Regular Article
  • 13 Downloads
Part of the following topical collections:
  1. Fractional Dynamical Systems - Recent Trends in Theory and Applications

Abstract

Fractional difference operators with discrete-Mittag-Leffler kernels of order α > 1 are defined and their corresponding fractional sum operators are confirmed. We prove existence and uniqueness theorems for the discrete fractional initial value problems in the frame of discrete Caputo (ABC) and Riemann (ABR) operators by using Banach contraction theorem. Then, we prove Lyapunov type inequality for a Riemann type fractional difference boundary value problem of order 2 < α < 5∕2 within discrete Mittag-Leffler kernels, where the limiting case α → 2+ results in the ordinary difference Lyapunov inequality. Examples are given to clarify the applicability of our results and an application about the discrete fractional Sturm-Liouville eigenvalue problem is analyzed.

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Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and General SciencesPrince Sultan UniversityRiyadhSaudi Arabia
  2. 2.Department of MathematicsUniversity of Mohamed BoudiafM’silaAlgeria
  3. 3.Laboratoire des Mathématiques Appliquées, Université de BejaiaBejaiaAlgeria

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