ADAMS–BASHFORTH NUMERICAL METHOD-BASED SOLUTION OF FRACTIONAL ORDER FINANCIAL CHAOTIC MODEL

Abstract

A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed model. To solve the financial chaotic model with nonlocal operators, the fractional Adams–Bashforth method (ABM) is applied based on Lagrange polynomial interpolation (LPI). The existence and uniqueness of the solution of the model can be demonstrated using fixed point theory and nonlinear analysis. Further, the error analysis of the present method and Ulam–Hyers stability of the considered model have also been included. Obtained numerical simulations reveal that the model based on three different fractional derivatives shows various chaotic behaviors that may be useful in a practical sense which may not be observed in the integer case.