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This article deals with numerical solution and identification of the fractional orders for the generalized nonlocal elastic model. Based on the collocation-finite difference scheme for the forward operator, a regularized method is proposed for solving of the forward problem with Tikhonov regularization, which gives a feasible approach to numerical solution of the nonlocal elastic model. The inverse problem of determining the fractional orders is solved by using the optimal perturbation algorithm with additional observations at some measurable points. The inversion solutions with noisy data give good approximations to the exact orders demonstrating the effectiveness of the numerical algorithms.

This article deals with an inverse problem of determining the diffusion coefficients in 2D fractional diffusion equation with a Dirichlet boundary condition by the final observations at the final t...

This paper deals with numerical solution for the space-time fractional diffusion equation with variable diffusion coefficient, and numerical inversion for the space-dependent diffusion coefficient by the homotopy regularization algorithm. An equivalent system to the forward problem is deduced by utilizing properties of the fractional derivatives, and an implicit finite difference scheme for solving the forward problem is set forth, and its stability and convergence are proved based on estimation to the spectrum radius of the coefficient matrix. The homotopy regularization algorithm is introduced to solve the inverse problem, and numerical inversions are performed with noisy data. The inversion solutions give good approximations to the exact solution as the noise level goes to small demonstrating a numerical stability of the inverse problem here.