A wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernel (Q2106214)

The paper focuses on the numerical solution of fourth-order time-fractional integro-differential equations defined on a rectangular domain and containing an integral operator with a weakly singular kernel. First, scaling functions are defined as Gegenbauer orthogonal polynomials, and the Riemann-Lieuville fractional integral operator for these scaling functions is expressed using the Laplace transform. Then, the authors use a collocation method with the Gegenbauer scaling functions and uniformly distributed collocation points to convert the problem into a system of linear algebraic equations. Furthermore, the authors establish error estimates for the operators involved and the truncation error estimate. Numerical experiments are presented to confirm the theoretical results.