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A grid method for solving the first boundary value problem for ordinary and partial differential equations with the Riemann–Liouville fractional derivative is justified. The algorithm is based on using Green’s function, the Fredholm integral equation, and the Lagrange interpolation polynomial. The impact of the Dirichlet boundary condition on the accuracy of the approximate solution is revealed and quantitatively described through the weight assessment. All the estimates provide clear evidence that the accuracy order of the grid method is higher near the boundary of the domain than it is in the inner nodes of the mesh set.

The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation