20 / 12 / 2022 - 16:00 – 16:30

Nasser H. Sweilam1, S. M. Al-Mekhlafi2 & N. R. Alsenaideh3

1 Faculty of Science, Cairo University

Numerical Studies of Climate Change Models under Piecewise Hybrid Fractional Derivative

Abstract

Many real-life problems have processes that exhibit crossover behavior. Modeling processes based on crossover behaviors has proven to be a difficult task for mankind. In various instances, real-world difficulties have been observed as a result of the transition from Markovian to randomness processes, such as in epidemiology with the spread of infectious illnesses and even some chaos. To build the future state of the system and unpredictability, deterministic and stochastic approaches were developed independently. In this talk, we extended two mathematical models of climate change by applying the piecewise differential equation system. The new hybrid fractional order operator can be written as a linear combination of the fractional order integral of Riemann-Liouville and the fractional order derivative Caputo is applied to extend the deterministic model and the fractional Brownian motion is applied to extend the stochastic differential equations. The positivity, boundedness, existence of the solutions for the model are discussed. New numerical algorithms are improved to solving the proposed model. Numerical examples and comparative studies for testing the applicability of the utilized method and to show the simplicity of this approximation approach are presented.