Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations

We give an effective method for solving fractional Riccati differential equations. We first define the fractional-order Boubaker wavelets (FOBW). Using the hypergeometric functions, we determine the exact values for the Riemann-Liouville fractional integral operator of the FOBW. The properties of FOBW, the exact formula, and the collocation method are used to transform the problem of solving fractional Riccati differential equations to the solution of a set of algebraic equations. These equations are solved via Newton's iterative method. The error estimation for the present method is also determined. The performance of the developed numerical schemes is assessed through several examples. This method yields very accurate results. The given numerical examples support this claim. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents an effective method for solving fractional Riccati differential equations by defining FOBW and using hypergeometric functions to transform the problem into a set of algebraic equations. The equations are solved using Newton's iterative method, with error estimation provided. The performance of the method is evaluated through multiple examples, showing very accurate results.