Research Highlights

Finite element approximation for time-fractional fourth-order problem with nonlocal diffusion: existence-uniqueness and error bounds

Authors :- J. P. Mandaliya; S. Chaudhary; D. Kumar

Publication :- International Journal of Computational Methods (World Scientific), 2026

In this paper, we consider a time-fractional fourth-order nonlocal problem with Navier boundary conditions. First, we discuss the existence–uniqueness of the weak solution at the continuous level using Faedo–Galerkin method. Then this fourth-order problem is transformed into a system of two second-order equations. For this system, a fully discrete scheme is proposed which comprises the standard finite element method and the L2-1σ scheme on the graded mesh. For the proposed scheme, we derive α-robust convergence estimates. Finally, numerical experiments are presented to validate the theoretical findings.