APPLICATION OF ADOMIAN DECOMPOSITION METHOD TO A GENERALIZED FRACTIONAL RICCATI DIFFERENTIAL EQUATION ($\psi$-FRDE)

Asrar Saleh Alsulami; Mariam Al-Mazmumy; Maryam Ahmed Alyami; Mona Alsulami

Asrar Saleh Alsulami Department ofMathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Mariam Al-Mazmumy Department ofMathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Maryam Ahmed Alyami Department ofMathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Mona Alsulami Department ofMathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia

Article ID: 2451

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Keywords: $\psi$-Caputo derivative; fractional nonlinear Riccati differential equation; Adomian decomposition method; semi-analytical method

Abstract

In this article, we generalize the fractional Riccati differential equations (FRDEs) by using a fractional derivative of a function with respect to another function ( $\psi$-Caputo derivative) and obtain $\psi$-FRDEs. Using the Adomian decomposition method (ADM) with Wazwaz modification, we solve the $\psi$-FRDEs semi-analytically. Comparing the solutions of the $\psi$-FRDEs with several functions of $\psi(x)$ and different values of fractional orders, we show that the presented method is efficient.

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