A Robust and higher order numerical technique for a time-fractional equation with nonlocal condition

This paper investigates a higher-order numerical technique for solving an inhomogeneous time fractional reaction-advection-diffusion equation with a nonlocal condition. The time-fractional operator involved here is the Caputo derivative. We discretize the Caputo derivative by an L1–2 formula, while the compact finite difference scheme approximates the spatial derivatives. The numerical approach is based on Taylor’s expansion combined with modified Gauss elimination. A thorough study demonstrates that the suggested approach is unconditionally stable. Tabular results show that the proposed scheme has fourth-order accuracy in space and \((3-\beta )\) $(3-\beta )$ -th-order accuracy in time. The numerical results of two test problems demonstrate the effectiveness and reliability of the theoretical estimates.