Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation

Abstract In this research, a compact combination of Chebyshev polynomials is created and used as spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method based on applying Petrov–Galerkin procedure to discretize differential problem into system linear algebraic equations with unknown expansion coefficients. Using efficient Gaussian elimination procedure, we solve obtained matrices particular pattern. L ∞ {L}_{\infty } 2 {L}_{2} norms estimate error bound. Three numerical examples were exhibited verify theoretical analysis efficiency newly developed algorithm.