Numerical solution of nonlinear fractional pantograph differential equations with boundary conditions using Jacobi polynomials

In this research, a numerical method based on Jacobi polynomials is introduced for solving nonlinear fractional pantograph differential equations with boundary conditions. First, the differential equation is presented as an equivalent Volterra-Fredholm integral equation. Then, Jacobi polynomials and Gauss-Jacobi quadrature formula together with the Newton-Cotes collocation points are used in order to transform the obtained integral equation into a system of nonlinear algebraic equations. Finally, by considering some examples and computing the L^"2" and L^∞ errors, the efficiency and accuracy of the proposed method are shown.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -