<p>Chebyshev polynomials of the seventh kind, a generalization of ultraspherical polynomials, are employed as basis functions to develop a pseudo-operational collocation method for approximating solutions to variable-order reaction-diffusion systems, including the Gray–Scott model and coupled Burgers’ model, and the variable-order mobile-immobile model as an advection-dispersion equation. The time-fractional derivatives are defined in the Caputo sense. Two-variable basis functions are used to construct pseudo-operational matrices of fractional and integer orders, transforming the original problem into a system of algebraic equations. Error bounds for the approximate solutions are estimated in a Chebyshev-weighted space. The effectiveness and accuracy of the proposed method are demonstrated through several numerical applications.</p>