Towards Solving Fractional Order Delay Variational Problems Using Euler Polynomial Operational Matrices

Abstract

     In this paper, we introduce an approximate method for solving fractional order delay variational problems using fractional Euler polynomials operational matrices. For this purpose, the operational matrices of fractional integrals and derivatives are designed for Euler polynomials. Furthermore, the delay term in the considered functional is also decomposed in terms of the operational matrix of the fractional Euler polynomials. It is applied and substituted together with the other matrices of the fractional integral and derivative into the suggested functional. The main equations are then reduced to a system of algebraic equations. Therefore, the desired solution to the original variational problem is obtained by solving the resulting system. Error analysis has been discussed. An illustrative example is given in order to illustrate that the proposed method is very accurate and efficient for solving such kinds of problems.