MMN-4637
An analytical approach for solving system of Riccati equations
Sondos Muhammed Syam; Zailan Siri; Ruhaila Md Kasmani;Abstract
In this paper, we investigate the solution of fractional system of Riccati equations. This system is important since it appears in several applications in science such as control theory. We use the operational matrix method to solve this system. The block-pulse operational matrices will initially assist in the reduction of the nonlinear fractional order Riccati-differential problem into an algebraic system. Benefits of this approach include inexpensive setup costs for the equations without the use of projection techniques like Galerkin, collocation, etc. In addition, we prove the convergence of the approximate solution using operational matrix method to the exact solution. Finally, we present two examples to provide numerical evidences to the efficiency of numerical approach used in this paper. We notice that the error is within $10^{-13}$. Also, the approximate solutions are convergent to the exact solutions for different values of $\gamma$. Moreover, the approximate solutions approach to the solution when $\gamma=1$ as $\gamma$ approaches to one.
Vol. 26 (2025), No. 2, pp. 1045-1059