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

Nguyen Duc Phuong, Nguyen Huy Tuan, Dumitru Baleanu and Tran Bao Ngoc

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: 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.

Keywords: Fractional derivative; ill-posed problem; Elliptic equation; Random noise; Regularized solution (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:54

DOI: 10.1016/j.amc.2019.05.029

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