Analysis of 3D IS-LM macroeconomic system model within the scope of fractional calculus

Abstract

A mathematical model providing an asymptotic description of macro-economic system is considered in this work. The system in general deals with performance, behaviour, decision-making of an economy as a whole and also the structure. Due to the complexities of this system, a more complex mathematical model is requested. In this work, we considered the extension of the model using some non-local differential operators and the stochastic approach where the given parameters are converted to normal distributions. We have presented the conditions of existence of uniquely exact solutions of the system using the fixed-point theorem approach. Each model is solved numerical via a newly introduced modified Adams-Bashforth for fractional differential equations. We presented numerical simulations for different values of fractional order. The models with the Atangana-Baleanu and Caputo differential operators provided us with new attractors. Keywords: Macro-economic system, Stochastic model, Singular and non-singular kernels, New adams-Bashforth for fractional differential equations