A NUMERICAL APPROXIMATION FOR SOLVING THE FRACTIONAL-ORDER RICCATI EQUATION

In this paper, is proposed a numerical approximation for solv- ingfractional Riccati equation. The our numerical method is based on fractional-order Muntz-Legendre functions to abtain a numerical approx- imation ofunknown functions. Also we use Caputo fractional derivative for fractionalcalculus. Finally, by applying the collocation method, The Riccati equationlead to a system of algebraic equations that easily solv- able. Some numericalexamples Show the eciency and accuracy of the present method.

Keywords:

Fractional Muntz-Legendre Functions (FMLFs) , Fractional-order Riccati Equation (FRE) , Caputo Fractional Derivative