The Existence and Uniqueness of Riccati Fractional Differential Equation Solution and Its Approximation Applied to an Economic Growth Model

Muhamad Deni Johansyah (), Asep Kuswandi Supriatna, Endang Rusyaman and Jumadil Saputra ()
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Muhamad Deni Johansyah: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia
Asep Kuswandi Supriatna: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia
Endang Rusyaman: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia
Jumadil Saputra: Faculty of Business, Economic and Social Development, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia

Mathematics, 2022, vol. 10, issue 17, 1-21

Abstract: This work proposes and investigates the existence and uniqueness of solutions of Riccati Fractional Differential Equation (RFDE) with constant coefficients using Banach’s fixed point theorem. This theorem is the uniqueness theorem of a fixed point on a contraction mapping of a norm space. Furthermore, the combined theorem of the Adomian Decomposition Method (ADM) and Kamal’s Integral Transform (KIT) is used to convert the solution of the Fractional Differential Equation (FDE) into an infinite polynomial series. In addition, the terms of an infinite polynomial series can be decomposed using ADM, which assumes that a function can be decomposed into an infinite polynomial series and nonlinear operators can be decomposed into an Adomian polynomial series. The final result of this study is to find a solution of the RFDE approach to the economic growth model with a quadratic cost function using the combined ADM and KIT. The results showed that the RFDE solution on the economic growth model using the combined ADM and KIT showed a very good performance. Furthermore, the numerical solution of RFDE on the economic growth model is presented at the end of this work.

Keywords: Riccati Fractional Differential Equation (RFDE); Kamal’s Integral Transform (KIT); Adomian decomposition method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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