Recovering solution of the Reverse nonlinear time Fractional diffusion equations with fluctuations data

Authors

Doan Thi Thanh Xuan Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-8809-6056
Vo Thi Thanh Ha Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-3594-7267

https://doi.org/10.61383/ejam.20231237

Keywords:

Riemann-Liouville, Regularized solution, Gaussian white noise, Ill-posed

Abstract

In this study, our focus is on obtaining an estimated solution for the nonlinear fractional time diffusion equation. Specifically, we have utilized the Riemann Liouville fractional derivative. Additionally, we have concerned Gaussian white noise in the input data. As we are aware, this problem is considered ill-posed according to Hadamard's definition. To tackle this problem, we have proposed a regularized solution and demonstrated the convergence between the mild solution and the regularized solution.

References

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Published

2023 Sep 09

How to Cite

[1]

T. X. Doan Thi and T. H. Vo Thi, “Recovering solution of the Reverse nonlinear time Fractional diffusion equations with fluctuations data”, Electron. J. Appl. Math., vol. 1, no. 2, pp. 60–70, Sep. 2023.