The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative

الملخص EN

We obtain the approximate analytical solution for the fractional quadratic Riccati differential equation with the Riemann-Liouville derivative by using the Bernstein polynomials (BPs) operational matrices.

In this method, we use the operational matrix for fractional integration in the Riemann-Liouville sense.

Then by using this matrix and operational matrix of product, we reduce the problem to a system of algebraic equations that can be solved easily.

The efficiency and accuracy of the proposed method are illustrated by several examples.