... on the Lagrange polynomial interpolation to approximate the Caputo derivative on the nonuniform mesh. The truncation error rate and the optimal grading constant of the approximation on a graded mesh are obtained as min { 4 − α , r α } and ( 4 − α ) / α , respectively, where α ∈ ( 0 , 1 ) is the order...

...Pari J. Kundaliya In this work, a time-fractional nonlocal diffusion equation is considered. Based on the L 2- 1 σ scheme on a graded mesh in time and the standard finite element method (FEM) in space, the fully-discrete L 2- 1 σ finite element method is investigated for a time-fractional nonlocal...