Numerical solution of fractional delay differential equation by shifted Jacobi polynomials

In this paper, the fractional delay differential equation (FDDE) is considered for the purpose to develop an approximate scheme for its numerical solutions. The shifted Jacobi polynomial scheme is used to solve the results by deriving operational matrix for the fractional differentiation and integration in the Caputo and Riemann–Liouville sense, respectively. In addition to it, the Jacobi delay coefficient matrix is developed to solve the linear and nonlinear FDDE numerically. The error of the approximate solution of proposed method is discussed by applying the piecewise orthogonal technique. The applicability of this technique is shown by several examples like a mathematical model of houseflies and a model based on the effect of noise on light that reflected from laser to mirror. The obtained numerical results are tabulated and displayed graphically.