Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem

In this paper, we present a well-organized method to estimate the one-dimensional fractional Rayleigh–Stokes model using construction of orthogonal Gegenbauer polynomials (GBPs) and Lagrange square interpolation time derivative. Therefore, design an authentic fast numerical calculation approach based on elaborated convergence rate recovery method. The matrix derivative operation GBP is gained by employing characteristic type polynomial. privilege orthogonality operational matrices, which reduces computation increases speed. Eventually, propose three examples check validity studies illustrate precision efficiency new approach.