Third-Kind Chebyshev Wavelet Method for the Solution of Fractional Order Riccati Differential Equations

Abstract

In this paper, we derive the numerical solutions of the various fractional-order Riccati type differential equations using the third-kind Chebyshev wavelet operational matrix of fractional order integration (C3WOMFI) method. The operational matrix of fractional order integration method converts the fractional differential equations to a system of algebraic equations. The third-kind Chebyshev wavelet method provides sparse coefficient matrices, therefore the computational load involved for this method is not as severe and also the resulting method is faster. The numerical solutions agree with the exact solutions for non-fractional orders, and also the solutions for the fractional orders approach those of the integer orders as the fractional order coefficient a approaches to 1.