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Analysis of nonlinear ordinary differential equations with the generalized Mittag-Leffler kernel
Abdon Atangana1,2, Jyoti Mishra3
1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.
Abstract:
The Picard iterative approach used in the paper to derive conditions under which nonlinear ordinary differential equations based on the derivative with the Mittag-Leffler kernel admit a unique solution. Using a simple Euler approximation and Heun's approach, we solved this nonlinear equation numerically. Some examples of a nonlinear linear differential equation were considered to present the existence and uniqueness of their solutions as well as their numerical solutions. A chaotic model was also considered to show the extension of this in the case of nonlinear systems.
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