Orthogonal polynomials

Algorithm

Discrete mathematics

Physics

Mathematical optimization

Mathematical analysis

Finite element method

Artificial intelligence

Fibonacci number

Galerkin method

Petrov–Galerkin method

Applied mathematics

Mathematics

Computer science

Wavelet

Numerical analysis

Fibonacci polynomials

Difference polynomials

Thermodynamics

Optimal Control Applications and Methods

Summary In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique.

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems