Regularization of nonlocal pseudo-parabolic equation with random noise

Authors

https://doi.org/10.61383/ejam.20231119

Keywords:

Fractional Tikhonov; Regularization; Conformable time derivative; Discrete data, random noise.

Abstract

In this paper, we consider an inverse problem for a time-fractional diffusion equation with the inhomogeneous source. These problems have many applications in engineering such as image processing, geophysics, biology. We get the result in random case as follows:

• This problem is ill-posed.

• We have used the nonlocal condition, instead of the final time condition.

• Using the IFT regularization method, constructing the regularized solution, the a-priori choice rule for the regularization parameter is discussed and yields the corresponding convergence rate.

• A numerical experiment is presented to illustrate the results in theory.

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Published

2023 May 08

How to Cite

[1]
Y. Gurefe, D. L. Le, and D. Kumar, “Regularization of nonlocal pseudo-parabolic equation with random noise”, Electron. J. Appl. Math., vol. 1, no. 1, pp. 40–61, May 2023.

Issue

Vol. 1 No. 1 (2023)

Section

Research Article

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Copyright (c) 2023 Yusuf Gurefe; Le Dinh Long (Corresponding Author); Devendra Kumar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
 
 
Received 2023 Mar 02
Accepted 2023 May 02
Published 2023 May 08

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