Solusi Persamaan Diferensial Fraksional Riccati Menggunakan Adomian Decomposition Method dan Variational Iteration Method

Muhamad Deni Johansyah, Herlina Napitupulu, Erwin Harahap, Ira Sumiati, Asep K. Supriatna

Abstract

Kata kunci: diferensial, fraksional, riccati, adomian dekomposisi

The solution of Riccati Fractional Differential Equation
using Adomian Decomposition method

Abstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations.  In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed.  The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM).  The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives.  The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically.

Keywords: riccati, fractional, differential, adomian, decomposition

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DOI: https://doi.org/10.29313/jmtm.v18i1.4931

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