Mittag - Leffler stability of systems of fractional nabla difference equations
Bull. Korean Math. Soc.
Published online 2018 Nov 08
Paul Eloe, and Jaganmohan Jonnalagadda
Birla Institute of Technology and Science Pilani, University of Dayton
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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