Finite Element Approximation of Time-Fractional Fourth-Order Problem with Nonlocal Diffusion: Existence–Uniqueness and Error Bounds

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 [Formula: see text] scheme on the graded mesh. For the proposed scheme, we derive [Formula: see text]-robust convergence estimates. Finally, numerical experiments are presented to validate the theoretical findings.