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 a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linear algebraic equations with unknown expansion coefficients. Using the efficient Gaussian elimination procedure, we solve the obtained system of equations with matrices of a particular pattern. The

and

L 2 {L}_{2}

norms estimate the error bound. Three numerical examples were exhibited to verify the theoretical analysis and efficiency of the newly developed algorithm.