Application of fractional differential equation in economic growth model: A systematic review approach

Muhamad Deni Johansyah; Asep K. Supriatna; Endang Rusyaman; Jumadil Saputra; Muhamad Deni Johansyah; Asep K. Supriatna; Endang Rusyaman; Jumadil Saputra

doi:10.3934/math.2021594

AIMS Mathematics

2021, Volume 6, Issue 9: 10266-10280. doi: 10.3934/math.2021594

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Mini review

Application of fractional differential equation in economic growth model: A systematic review approach

1.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
2.
School of Social and Economic Development, Universiti Malaysia Terengganu, Malaysia

Received: 03 June 2021 Accepted: 07 July 2021 Published: 12 July 2021
MSC : 26A33, 34A08, 34A34, 34B10

In this paper we review the applications of fractional differential equation in economic growth models. This includes the theories about linear and nonlinear fractional differential equation, including the Fractional Riccati Differential Equation (FRDE) and its applications in economic growth models with memory effect. The method used in this study is by comparing related literatures and evaluate them comprehensively. The results of this study are the chronological order of the applications of the Fractional Differential Equation (FDE) in economic growth models and the development on theories of the FDE solutions, including the FRDE forms of economic growth models. This study also provides a comparative analysis on solutions of linear and nonlinear FDE, and approximate solution of economic growth models involving memory effects using various methods. The main contribution of this research is the chonological development of the theory to find necessary and sufficient conditions to guarantee the existence and uniqueness of the FDE in economic growth and the methods to obtain the solution. Some remarks on how further researches can be done are also presented as a general conclusion.
- Fractional Order Derivative (FDE),
- differential equation,
- Fractional Riccati Differential Equation (FRDE),
- economic growth model,
- memory effect modeling
Citation: Muhamad Deni Johansyah, Asep K. Supriatna, Endang Rusyaman, Jumadil Saputra. Application of fractional differential equation in economic growth model: A systematic review approach[J]. AIMS Mathematics, 2021, 6(9): 10266-10280. doi: 10.3934/math.2021594

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Abstract

In this paper we review the applications of fractional differential equation in economic growth models. This includes the theories about linear and nonlinear fractional differential equation, including the Fractional Riccati Differential Equation (FRDE) and its applications in economic growth models with memory effect. The method used in this study is by comparing related literatures and evaluate them comprehensively. The results of this study are the chronological order of the applications of the Fractional Differential Equation (FDE) in economic growth models and the development on theories of the FDE solutions, including the FRDE forms of economic growth models. This study also provides a comparative analysis on solutions of linear and nonlinear FDE, and approximate solution of economic growth models involving memory effects using various methods. The main contribution of this research is the chonological development of the theory to find necessary and sufficient conditions to guarantee the existence and uniqueness of the FDE in economic growth and the methods to obtain the solution. Some remarks on how further researches can be done are also presented as a general conclusion.

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