Fractional Calculus: New Applications in Understanding Nonlinear Phenomena

Complex Chaotic Fractional-order Finance System in Price Exponent with Control and Modeling

Author(s): Muhammad Farman, Parvaiz Ahmad Naik*, Aqeel Ahmad, Ali Akgul and Muhammad Umer Saleem

Pp: 61-84 (24)

DOI: 10.2174/9789815051933122030006

* (Excluding Mailing and Handling)


The present chapter proposes modeling of complex fractional-order chaotic ifnancial system with control. Here, we have added critical minimum interest rate ‘d’ as a new parameter to get a novel stable ifnancial model. The fractional derivatives. are taken in Caputo and Caputo-Fabrizio sense for the proposed ifnance system. Dynamical models in ifnancial system with complicated behavior provide a new. perspective as result of trends and actual behavior of internal structure of the ifnancial. system. A theoretical stabilization of the equilibria, as well as the numerical simulations, are obtained. Furthermore, with sensitivity analysis, a certain threshold estimation of the basic reproductive number has been made. Also, the stability analysis of the model, together with uniqueness of the special solutions is provided. The concept of controllability and observability for the linearized control model is used for feedback control. The solution of the proposed fractional-order model has been procured by employing different numerical techniques with comparison among the solutions. The convergence analysis is carried out for the accuracy of the applied scheme. Finally, some numerical simulations are given for three fractional-order chaotic systems to verify the efectiveness for the obtained results. The fractal, stochastic processes and prediction are used in particular mechanism of its application to the macro and micro processes.

Keywords: Complex chaotic system, Caputo derivative, Caputo-Fabrizio derivative, Dynamical control, Fixed point theorem, Fractional-order ifnance. system, Stability analysis.

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