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

y-Caputo derivative, fractional nonlinear Riccati differential equation, Adomian decomposition method, semi-analytical method.

Received: August 4, 2024; Revised: August 22, 2024; Accepted: August 31, 2024; Published: September 25, 2024

How to cite this article: Asrar Saleh Alsulami, Mariam Al-Mazmumy, Maryam Ahmed Alyami and Mona Alsulami, Application of Adomian decomposition method to a generalized fractional Riccati differential equation (y-FRDE), Advances in Differential Equations and Control Processes 31(4) (2024), 531-561. https://doi.org/10.17654/0974324324028

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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