The time-fractional Sobolev equations in two and three dimensions are investigated for numerical solutions using a relatively new computational methodology. The Caputo derivative is used for the time-fractional part of the problem, which is subsequently coupled with a splitting technique. For the spatial derivatives, a meshless collocation method based on Fibonacci and Lucas polynomials is utilized. These Lucas and Fibonacci polynomials are non-orthogonal and eliminate the need for interval transformations, facilitating the efficient approximation of higher-order derivatives for unknown functions. To validate the accuracy of the proposed method, various error norms are applied across both regular and irregular domains. Additionally, the results obtained using the proposed method are also compared with the exact solution and other numerical techniques documented in recent studies.
Ahmad et al. (Fri,) studied this question.