A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

Implicit hybrid methods for solving fractional Riccati equation

“…Fractional Riccati equation plays an important role in several physical and engineering applications. Since it is not easy task to find the exact solution of the fractional Riccati equation, several researchers investigated its solution numerically such as the Legendre wavelet operational matrix method [3], Adomian decomposition method [18], homotopy perturbation method [13], the Laplace transform and homotopy perturbation method [2], fractional Chebyshev finite difference method [10], the polynomial least squares method [4], and the Bezier curves [7]. In addition, artificial neural networks [20], the optimal homotopy asymptotic method [8] and the Laplace-Adomian-Pade method [12], Bäcklund transformation [17], and He's variational iteration method [9], are used to solved this problem.…”

An Investigation on an Optimal Control Problem with a Fractional Constraint in the Riemann-Liouville Sense

“…However, in non-integer order problems in the sense of singular differential operators, the numerical investigations demands special care while the singularity of a kernel in a definition of some fractional operators, could not be handled by many classical theorems. In this way, some new approaches and techniques are introduced (see for example [7,8]). …”

A numerical method for solving singular Riccati equation with fractional order by modified fractional power series method

“…The numerical solution of the fractional Riccati differential equation was discussed by several researchers. Some of these numerical techniques are the polynomial least squares method [8], Adomian decomposition method [9], Bernstein polynomials [10], Legendre wavelet operational matrix method [11], and Bezier curves method [12]. Syam [13] solved the fractional Riccati differential equation by the fractional-order Legendre operational matrix of fractional integration.…”