10.71932/

Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability

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  • Ndolane Sene1,
  1. Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, BP 5683 Dakar Fann, Senegal

Published in Issue 12-07-2025

Copyright (c) 2025 Ndolane Sene (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Sene, N. (2025). Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability. International Journal of Mathematical Modelling & Computations, 10(01). https://doi.org/10.71932/
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Abstract

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional differential equation using the generalized Mittag-Leffler input stability of the sub-fractional differential equations. In other words, we prove a cascade of fractional differential equations, which are generalized Mittag-Leffler input stables and governed by a fractional differential equation, which is generalized Mittag-Leffler stable, is generalized Mittag-Leffler stable. We give Illustrative examples to illustrate our main results. Note in our paper; we use the generalized fractional derivative in Caputo-Liouville sense. 

Keywords

  • Mittag-Leffler stability,
  • Generalized fractional derivatives,
  • Input stability
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