Chebyshev spectral methods for multi-order fractional neutral pantograph equations

This paper is concerned with the application of the spectral tau and collocation methods to delay multi-order fractional differential equations with vanishing delayrx(0<r<1)The fractional derivatives are described in the Caputo sense. The model solution is expanded in terms of Chebyshev polynomials. The convergence of the proposed approaches is investigated in the weightedL2-norm. Numerical examples are provided to highlight the convergence rate and the flexibility of this approach. Our results confirm that nonlocal numerical methods are best suited to discretize fractional differential equations as they naturally take the global behavior of the solution into account.