An approximate solution of fractional order Riccati equations based on controlled Picard’s method with Atangana–Baleanu fractional derivative

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 0<α<1. 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.

Keywords

• Fractional differential equations
• Atangana–Baleanu derivative
• Picard’s method
• Riccati equation