Numerical Solution of the Fractional Dynamics of a Surface Energy Balance-Mass Balance Model of Cryosphere

Abstract

In the present task, the dynamics of Cryosphere is represented based on the modified Caputo-Fabrizio fractional derivative. A numerical scheme based on the fifth-order fractional Adams-Bashforth approach is applied to the dynamical system of the proposed model. The nonlinear system of differential equations of arbitrary order in the model is described by the modified Caputo-Fabrizio fractional operator, and the model has been checked for non-zero outcomes under the non-singular fractional operator. Existence and uniqueness of the given fractional model is discussed. The scheme’s stability analysis is checked. All model findings are sketched with the application of MATLAB R2016a mathematical software. The novelty of this work lies in using fractional order five-step Adams-Bashorth method in order to approximate the surface energy balance-mass balance fractional model of the Cryosphere. We represent the system using Caputo-Fabrizio fractional differential equations.