This paper presents a new numerical method for solving fractional optimal control problems (FOCPs). The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon Bernoulli polynomials. The operational matrices of fractional Riemann–Liouville integration and multiplication for Bernoulli polynomials are derived. The error upper bound for the operational matrix of the fractional integration is also given. The properties of Bernoulli polynomials are utilized to reduce the given optimization problems to the system of algebraic equations. By using Newton’s iterative method, this system is solved and the solution of FOCPs are achieved. Illustrative examples are included to demonstrate the validity and applicability of the technique.

An approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev (RC) tau method. The operational matrices of the derivative and product of RC functions are presented. These matrices together with the tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

A method for solving the nonlinear second‐order Fredholm integro‐differential equations is presented. The approach is based on a compactly supported linear semiorthogonal B‐spline wavelets. The operational matrices of derivative for B‐spline scaling functions and wavelets are presented and utilized to reduce the solution of Fredholm integro‐differential to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.