Nguyen Huy TuanBaleanu, DumitruTran Bao NgocNguyen Duc Phuong02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2020-01-302025-09-182020-01-302025-09-182019Nguyen Duc Phuong; Nguyen Huy Tuan...et al. (2019). "On Cauchy problem for nonlinear fractional differential equation with random discrete data", Applied Mathematics and Computation, Vol. 362.0096-30031873-5649https://doi.org/10.1016/j.amc.2019.05.029https://hdl.handle.net/123456789/10627Phuong, Nguyen Duc/0000-0003-3779-197X; Nguyen Huy, Tuan/0000-0002-6962-1898; Tran Bao, Ngoc/0000-0003-1600-5845This 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 L-2 and H-q (for q > 0) norm. Moreover, the numerical example is also investigated to justify our results. (C) 2019 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessFractional DerivativeIll-Posed ProblemElliptic EquationRandom NoiseRegularized SolutionArticle10.1016/j.amc.2019.05.0292-s2.0-85068465841