This paper will give the numerical difference scheme with Dirichlet boundary condition, and prove stability and convergence of the difference scheme, final numerical experiment results also confirm effectiveness of the algorithm. KeywordsFractional derivative; Numerical difference scheme; The gradient regularization method.

In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agr...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...