In this article, a modified implicit hybrid method for solving the fractional Bagley-Torvik boundary (BTB) value problem is investigated. This approach is of a higher order. We study the convergence, zero stability, consistency, and region of absolute stability of the modified implicit hybrid method. Three of our numerical examples are presented.

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.

In this paper, we study the singular Riccati equation with fractional order. The modified fractional power series method (MFPS) is used to solve the proposed problem. The validity of the MFPS method is ascertained by presenting several examples. We prove the existence of the solution of the Riccati equation with fractional order. The convergence of the approximate solution using the proposed method is investigated. Theoretical and numerical results are presented.