An approximate solution of fractional order Riccati equations based on controlled Picard’s method with Atangana–Baleanu fractional derivative
Alexandria Engineering Journal • 2022
Publication Information
Authors
Fareed, A.F., Semary, M.S., Hassan, H.N.
Keywords
Fractional differential equations Atangana–Baleanu derivative Picard’s method Riccati equation
Journal
Alexandria Engineering Journal
Publisher
Elsevier
Volume
61
Issue
5
Pages
3673-3678
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
In this paper, a new computationally efficient approach to solve fractional differential equations with Atangana–Baleanu operator is introduced. Controlled Picard’s method is employed for solving a class of fractional differential equations with order . The proposed approach can cover wide range of integer and fractional orders differential equations due to the extra auxiliary parameter which enhances the convergence and is suitable for nonlinear differential equations. Two models of fractional Riccati equation are solved to validate and illustrate the accuracy of the new approach. Figures has been used to construct the results obtained from the presented approach. It is shown that the proposed method is efficient, credible, and easy to implement for various related problems in science and engineering.
Staff Members - Benha University