Regularization of nonlocal pseudo-parabolic equation with random noise

Authors

DOI:

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.

References

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Published

2023 May 08

Issue

Vol. 1 No. 1 (2023)

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Research Article

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

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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.
 
 

How to Cite

[1]
“Regularization of nonlocal pseudo-parabolic equation with random noise”, Electron. J. Appl. Math., vol. 1, no. 1, pp. 40–61, May 2023, doi: 10.61383/ejam.20231119.

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