A wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernel
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.
scientific article; zbMATH DE number 7630330
scientific article