Mittag-Leffler stability of systems of fractional nabla difference equations
Bull. Korean Math. Soc. 2019 Vol. 56, No. 4, 977-992
Published online July 9, 2019
Printed July 31, 2019
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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