| Abstract: |
| In this study, we explore the solution of a fractional system of Riccati equations, which plays a significant role in various scientific applications, including control theory. To address this system, we employ the operational matrix method. Initially, the block-pulse operational matrices aid in transforming the nonlinear fractional-order Riccati-differential problem into a system of algebraic equations. One of the key advantages of this approach is that it offers a cost-effective framework for setting up the equations without relying on projection methods such as Galerkin, collocation, or similar techniques. Furthermore, we establish the convergence of the approximate solution obtained through the operational matrix method toward the exact solution. To demonstrate the efficacy of the proposed numerical method, we present two illustrative examples. The results show that the error is on the order of $\mathcal{O}(10^{-13})$. Additionally, the approximate solutions are shown to converge to the exact solutions for various values of $\gamma$. As $\gamma$ approaches one, the approximate solutions increasingly align with the solution for $\gamma = 1$. |
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