A shifted Chebyshev operational matrix method for pantograph-type nonlinear fractional differential equations

In this study, we investigate and analyze an approximation of the Chebyshev polynomials for pantograph-type fractional-order differential equations. First, we construct the operational matrices of pantograph and Caputo fractional derivatives using Chebyshev interpolation. Then, the obtained matrices are utilized to approximate the fractional derivative. We also provide a detailed convergence analysis in terms of the weighted square norm. Finally, we describe and discuss the results of three numerical experiments conducted to confirm the applicability and accuracy of the computational scheme.