Regularization of nonlocal pseudo-parabolic equation with random noise

Authors

Yusuf Gurefe Department of Mathematics, Faculty of Science, Mersin University, Mersin, Turkey https://orcid.org/0000-0002-7210-5683
Le Dinh Long Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam https://orcid.org/0000-0001-8805-4588
Devendra Kumar Department of Mathematics, University of Rajasthan, Jaipur-302004, India https://orcid.org/0000-0003-4249-6326

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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