Bernoulli polynomial based wavelets method for solving chaotic behaviour of financial model

Abstract

This paper presents an algorithm for solving systems of non integer financial chaotic model. The Bernoulli wavelets function approximation applies to fractional order financial systems for the first time. The main objective of this process is to convert fractional differential equation systems into algebraic equation systems using wavelets approximation based on Bernoulli wavelets and their fractional integral operators. This fractional financial chaotic model that represents the effects of memory and chaos in a system. There are 3 compartments in this fractional order financial system: price indexes, interest rates, and investment demand. Analyses are depends on iteration method and Bernoulli wavelets method to determine the stability analysis, residual error and convergence analysis of the solutions. This study indicates that the presented approximate solutions fit exactly with the numerical solution and that the technique is accurate and effective. Our proposed model has been discussed for its uniqueness, boundedness, and non negativity. Its findings are extremely important for dealing with financial issues in the future.