Analysis of Riccati Fractional Differential Equation Solution Using Variation of Parameters Method and Kamal Decomposition Method

Abstract

A differential equation is an equation that involves the derivative of one or more dependent variables on one or more independent variables. Based on the form of the function, power, and coefficients, differential equations are classified into linear and non-linear. Differential equations generally have the order of natural numbers, but with the study of fractional calculus, differential equations developed into fractional order form which are called Fractional Differential Equations (FDEs). One form of non-linear FDEs is Riccati's FDEs. Many methods have been used to solve Riccati's FDEs, one of which is the Variation of Parameters Method (VPM) and Kamal Decomposition Method. The purpose of this research is to find an approximate solution of PDF Riccati using these two methods, then a comparison analysis based on Mean Absolute Error (MAE) is carried out to find out which method is more accurate. In this research, two forms of Riccati’s FDEs problems were taken. Furthermore, the two forms of problems are sought for approximate solutions until the third iteration and further simulated with graphs using Maple 18 until the fifth iteration. Based on the comparison analysis, the Riccati’s FDEs approximation solutions of the two problem forms obtained using VPM are more accurate than the Kamal Decomposition Method.