Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with Mittag-Leffler memory

In this paper, we consider two accurate iterative methods for solving fractional differential equations with power law and Mittag-Leffler kernel. We focused our attention on the stage-structured prey-predator model and several chaotic attractors of type Newton-Leipnik, Rabinovich-Fabrikant, Dadras, Aizawa, Thomas' and 4 wings. The first algorithm is based on the trapezoidal product-integration rule, and the second one is based on Lagrange interpolations. The results obtained show that both numerical methods are very efficient and provide precise and outstanding results to determine approximate numerical solutions of fractional differential equations with non-local singular kernels.

Automated summary

This paper considers two accurate iterative methods for solving fractional differential equations with power law and Mittag-Leffler kernel, focusing on the stage-structured prey-predator model and several chaotic attractors. The results obtained show that both numerical methods are very efficient and provide precise and outstanding results for approximate numerical solutions of fractional differential equations with non-local singular kernels.