New solutions of fractional 4D chaotic financial model with optimal control via He-Laplace algorithm

Abstract

The objective of current investigation is to propose a solution to predict the interest rate, investment demand, and price index with optimal control in a fractional financial 4D chaotic model. He-Laplace method (HLM) is introduced with fractional derivative in Caputo sense to characterize the memory effect of the 4D chaotic model. For validation and comparison purposes, the given financial model is also solved through fractional residual power series algorithm. Analysis revealed that HLM provide improved results as compared to RPSA. Model is also analyzed graphically for interest rate, investment demand, price index and input control in fractional environment to understand the physical behavior of the model. The impact of variations in saving amount, cost per investment, and elasticity in demand are also presented through contours. It is reported that initially the interest rate, investment demand and price index are uniform, but later on drastic increase have been observed. Analysis also revealed that proposed methodology is stable and performed exceptionally well in chaotic scenarios, and hence can be extended to other complex models.

Keywords

• 4D chaotic financial model
• Caputo fractional derivative
• Laplace transform
• Homotopy perturbation
• Residual power series