Error estimate of finite element/finite difference technique for solution of two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives

Abstract

In the current investigation, an error estimate has been proposed to solve the two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives based on the finite element/finite difference scheme. The time and space derivatives are based on the Riemann–Liouville and Riesz fractional derivatives, respectively. At first, the temporal variable has been discretized by a second-order difference scheme and then the space variable has been approximated by the finite element method (FEM). The analytical study shows that the presented scheme is unconditionally stable and convergent. Finally, some examples have been introduced to confirm the theoretical results and efficiency of the proposed technique.