Sine-cosine wavelet operational matrix of fractional order integration and its applications in solving the fractional order Riccati differential equations

Abstract

Abstract In this paper, the sine-cosine wavelet method is presented for solving Riccati differential equations. The sine-cosine wavelet operational matrix of fractional integration is derived and utilized to transform the equations to system of algebraic equations. Also, the error analysis of the sine-cosine wavelet bases is given. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. Some examples are included to demonstrate the validity and applicability of the technique.

Keywords

• fractional calculus
• sine-cosine wavelet
• operational matrix
• Riccati differential equations
• numerical method