Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(4): 977-992

Online first article July 9, 2019      Printed July 31, 2019

https://doi.org/10.4134/BKMS.b180749

Copyright © The Korean Mathematical Society.

Mittag-Leffler stability of systems of fractional nabla difference equations

Paul Eloe, Jaganmohan Jonnalagadda

University of Dayton; Birla Institute of Technology and Science Pilani

Abstract

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

Keywords: fractional order nabla difference, discrete Mittag-Leffler function, discrete exponential function, $N$-transform, Mittag-Leffler stability

MSC numbers: 39A30, 39A12, 34A08

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