Solving the Economic Growth Acceleration Model with Memory Effects: An Application of Combined Theorem of Adomian Decomposition Methods and Kashuri–Fundo Transformation Methods

Muhamad Deni Johansyah,Endang Rusyaman,Asep K Supriatna,Jumadil Saputra

doi:10.3390/sym14020192

Muhamad Deni Johansyah, Endang Rusyaman + Show 2 more

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https://doi.org/10.3390/sym14020192

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Journal: Symmetry	Publication Date: Jan 19, 2022
Citations: 4	License type: CC BY 4.0

Affiliation: Padjadjaran University, Universiti Malaysia Terengganu

Abstract

The primary purpose of this study is to solve the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using Combined Theorem of Adomian Polynomial Decomposition and Kashuri–Fundo Transformation methods. The economic growth model (EGM) with memory effects for the quadratic cost function is analysed by modifying the linear fractional differential equation. The study’s significant contribution is to develop a linear cost function in the EGM for a quadratic non-linear cost function and determine the specific conditions of the Riccati fractional differential equation (RFDEs) in the EGM with memory effects. The study results showed that RFDEs in the EGM involving the memory effect have a solution and singularity. Additionally, this study presents a comparison of exact solutions using Lie symmetry, Combined Theorem of Adomian Polynomial Decomposition, and Kashuri–Fundo Transformation methods. The results showed that the three methods have the same solution. Furthermore, this study provides a numerical solution to the RFDEs on the EGM with memory effects. The numerical simulation results showed that the output value of Y(t) for the quadratic cost function in the economic growth model is significantly affected by the memory effect.

Highlights

IntroductionThe differential equation (DE) has been widely investigated in many scientific fields and technological applications, including, economic [1] and financial models [2], pest management [3], accounting [4], supply chain system [5], biology [6], chemistry [6], electrochemistry [7], electronic circuit [8], memristors [9], mechanical models [10], encryption [11], robotics [12] and engineering application [13,14,15].Some studies related to the Adomian Decomposition Method (ADM) can be seen inRefs. [16,17,18,19,20,21]
The graph is close to the exact solution, which shows that the output value Y(t) for the quadratic cost function in the economic growth model is significantly affected by the memory effect
This paper has successfully developed the Riccati fractional differential equation in the new economic growth acceleration model with a memory effect for the quadratic cost function

Summary

Introduction

The differential equation (DE) has been widely investigated in many scientific fields and technological applications, including, economic [1] and financial models [2], pest management [3], accounting [4], supply chain system [5], biology [6], chemistry [6], electrochemistry [7], electronic circuit [8], memristors [9], mechanical models [10], encryption [11], robotics [12] and engineering application [13,14,15].Some studies related to the Adomian Decomposition Method (ADM) can be seen inRefs. [16,17,18,19,20,21]. Some studies related to the Adomian Decomposition Method (ADM) can be seen in. Bhakelar and Listdar-Gejji [16] employed the ADM and homotopy perturbation technique (HPM) for solving the logistic fractional differential equation (FDE). Mahdy and Marai [17] obtained the approximate solution of RFDE using the combination of ADM and Sumudu integral transformation (SIT). Hu et al [18] proposed the ADM for solving the linear fractional differential equation (FDE), and Daftardar-Gejji and Jafari [19] applied the ADM to obtain a solution to multi-order FDE. Bildik and Bayramoglu [20]

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