On Cauchy problem for nonlinear fractional differential equation with random discrete data

摘要

This paper is concerned with finding the solution u(x, t) of the Cauchy problem for nonlinear fractional elliptic equation with perturbed input data. This study shows that our forward problem is severely ill-posed in sense of Hadamard. For this ill-posed problem, the trigonometric of non-parametric regression associated with the truncation method is applied to construct a regularized solution. Under prior assumptions for the exact solution, the convergence rate is obtained in both L2 and Hq (for q > 0) norm. Moreover, the numerical example is also investigated to justify our results.