finite difference and local discontinuous galerkin methods for fourth-order time-fractional partial integro-differential equation: computational approach for one-dimensional case

‎‎our focus in this paper is on numerically solving fourthorder time-fractional integro-differential equations with weakly  singular kernels. l1 and quadrature formulas are used to discretize  the temporal and memory terms. for spatial discretization, a highorder local discontinuous galerkin method is employed. finally, the numerical optimal convergence rate for the proposed scheme is demonstrated by the use of numerical results.