A NUMERICAL APPROXIMATION FOR SOLVING THE FRACTIONAL-ORDER RICCATI EQUATION

Abstract

In this paper, is proposed a numerical approximation for solving fractional Riccati equation. The our numerical method is based on fractional-order Muntz-Legendre functions to abtain a numerical approximation of unknown functions. Also we use Caputo fractional derivative for fractional calculus. Finally, by applying the collocation method, The Riccati equation lead to a system of algebraic equations that easily solvable. Some numerical examples Show the efficiency and accuracy of the present method.