Crossover dynamics of climate change models: Numerical simulations

In this paper, two new climate change mathematical models are extended using the stochastic-deterministic piecewise hybrid fractional derivatives, where the hybrid fractional order operator is applied to extend the deterministic model and the fractional Brownian motion operator is applied to extend the stochastic model. The steady states analysis of the propsed models are discussed. Two numerical methods are constructed to study the behavior of the proposed models. These methods are Caputo proportional constant Adams-Bashfourth fifth step method for solving the hyprid fractional deterministic model and the modified nonstandard Euler Maruyama technique to study numerically the fractional Brownian motion stochastic model. Several numerical test examples are given to demonstrate the efficiency of the methods and to support the theoretical results.& COPY; 2023 The Authors. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).