Abstract
Abstract In this paper, theoretical estimates for the solution of an approximation problem for a fourth-order partial differential equation with fractional derivatives in the sense of Caputo are obtained. This equation describes a transient fluid flow in a fractured porous medium. To approximate fractional derivatives, a higher-order formula was applied, and a substep scheme technique was employed to retain a global higher-order convergence in the temporal variable. The method of a priori estimates is utilized to prove the unconditional stability of the proposed method with respect to the initial data and the right-hand side of the equation. The convergence of the approximate solution to the weak solution of the original differential problem is rigorously proved.