A new financial chaotic model in Atangana-Baleanu stochastic fractional differential equations
Chen Liping, Muhammad Altaf Khan, Abdon Atangana, Sunil Kumar
Abstract
We formulate and analyze a new financial chaotic model in fractional stochastic differential equation in Atangana-Baleanu operator. The model is constructed initially in integer case and then the application of fractional and stochastic approach are used for the model generalization. We study with care some of the mathematical results for the model in integer case by identifying the suitable values of parameters and initial values for the state variables for which the model behaves chaotic. Further, using the concept of stochastic differential equation, the model is further extended to the stochastic fractional differential equations. The equilibriums possibly the model posses are shown and analyzed. Lyapanove exponent are investigated for the model. We give a new method that is introduced recently in literature to find the model solution numerically for the case of fractional stochastic differential equation. We obtained many interesting graphical results for the model by considering different scenarios.