In this article, we develop a new set of functions called fractional-order Alpert multiwavelet
functions to obtain the numerical solution of fractional pantograph differential equations
(FPDEs). The fractional derivative of Caputo type is considered. Here we construct the
Riemann–Liouville fractional operational matrix of integration (Riemann–Liouville FOMI)
using the fractional-order Alpert multiwavelet functions. The most important feature
behind the scheme using this technique is that the pantograph equation reduces to a
system of linear or nonlinear algebraic equations. We perform the error analysis for the
proposed technique. Illustrative examples are examined to demonstrate the important
features of the new method.