Implicit hybrid methods for solving fractional Riccati equation

Abstract

In this paper, we modify the implicit hybrid methods for solving fractional Riccati equation. Similar methods are implemented for the ordinary derivative and we are the first who implement it for fractional derivative case. This approach is of higher order comparing with the existing methods in the literature. We study the convergence, zero stability, consistency, and region of absolute stability. Numerical results are presented to show the efficiency of the proposed method.

Solving Fractional Riccati Differential Equation with Caputo-Fabrizio Fractional Derivative

“…Which is compatible with the one found in [36], [33], [43], [40], [35], [26]. This example is classified as case 2.…”

“…The Riccati differential equation is employed across diverse disciplines like physics, engineering, biology, control theory, signal processing, and finance [25], [6], [20]. The fractional Riccati equation holds significance in numerous physics and engineering contexts [36], [33], [43], [40], [8], [11], [23], [35], [45]. Many investigators have examined the numerical solution of this problem [24], [22], [21], [30], [42], [5], [7].More convenientreferences for this equation can be found in [18], [37], [1], [30], [38], [27].…”