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Mathematical analysis and numerical simulation of time-fractional host-parasitoid system with Caputo operator

Owolabi Kolade M., Pindza Edson

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 1

79--90

In this paper, a time-fractional host-parasitoid dynamics which is regarded as a new variant of the novel Nicholson-Bailey model is considered in the sense of the Caputo operator. The model equation is examined for linear stability analysis to guide in ensuring the best choice of parameters when simulating the full dynamical system. Furthermore, this work provides a suitable numerical technique for the approximation of the Caputo fractional derivative with order ρ ∈ (0, 1]. To explore the dynamic richness of the model, numerical results are provided for different values of α.

Robust synchronization of chaotic fractional-order systems with shifted Chebyshev spectral collocation method

Owolabi Kolade M.

Journal of Applied Analysis

2021

Vol. 27, nr 2

269--282

In this work, synchronization of fractional dynamics of chaotic system is presented. The suggested dynamics is governed by a system of fractional differential equations, where the fractional derivative operator is modeled by the novel Caputo operator. The nature of fractional dynamical system is non-local which often rules out a closed-form solution. As a result, an efficient numerical method based on shifted Chebychev spectral collocation method is proposed. The error and convergence analysis of this scheme is also given. Numerical results are given for different values of fractional order and other parameters when applied to solve chaotic system, to address any points or queries that may occur naturally.