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

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.

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

“…There are many different studies in the literature that reveal the accuracy of these statements [11][12][13][14][15][16][17][18][19][20][21]. There are many studies that show that it gives effective results when used by blending with different methods to reach solutions of nonlinear and fractional differential equations [22][23][24][25][26][27][28][29][30][31][32]. In this study, we demonstrate that the Kashuri Fundo transform, based on Newton's cooling law, which is modeled with first-order differential equations, is an effective, reliable and time-saving method for reaching solutions of first-order differential equations.…”

Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform

“…Kashuri Fundo transform was introduced to the literature by Kashuri and Fundo with the statement that various properties can be found easily due to its deep connection with Laplace transform [2]. In later processes, many researchers, including Kashuri and Fundo, worked on different applications [6][7][8][9][10][11][12][13][14][15][16] of this transform. Helmi et al [17], Singh [18], Dhange [19], and Güngör [20] investigated various applications of Kashuri Fundo transformation.…”

Editorial Conclusion for the Special Issue “Applications of Symmetric Functions Theory to Certain Fields”

“…Their significant contribution was 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 equations (RFDEs) in the EGM with memory effects. The results given in [3] showed that RFDEs in the EGM involving the memory effect have a solution and singularity. Additionally, the paper presented a comparison of exact solutions using Lie symmetry and a combined theorem of Adomian polynomial decomposition and Kashuri-Fundo transformation methods.…”

“…Several examples were also given, including special functions, such as Bessel, Struve, Lommel, and q-Bessel functions. Johansyah et al [3] solved the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using a combined theorem of Adomian polynomial decomposition and Kashuri-Fundo transformation methods. They analysed the economic growth model (EGM) with memory effects for the quadratic cost function by modifying the linear fractional differential equation.…”