Modal spectral Tchebyshev Petrov–Galerkin stratagem for the time-fractional nonlinear Burgers’ equation

Herein, we construct an explicit modal numerical solver based on the spectral Petrov–Galerkin method via a specific combination of shifted Chebyshev polynomial basis for handling the nonlinear time-fractional Burger-type partial differential equation in the Caputo sense. The process reduces the problem to a nonlinear system of algebraic equations. Solving this algebraic equation system will yield the approximate solution’s unknown coefficients. Many relevant properties of Chebyshev polynomials are reported, some connection and linearization formulas are reported and proved, and all elements of the obtained matrices are evaluated neatly. Also, convergence and error analyses are established. Various illustrative examples demonstrate the applicability and accuracy of the proposed method and depict the absolute and estimated error figures. Besides, the current approach’s high efficiency is proved by comparing it with other techniques in the literature.