Determine unknown source problem for time fractional pseudo-parabolic equation with Atangana-Baleanu Caputo fractional derivative

Nguyen Duc Phuong; Le Dinh Long; Devender Kumar; Ho Duy Binh; Nguyen Duc Phuong; Le Dinh Long; Devender Kumar; Ho Duy Binh

doi:10.3934/math.2022883

AIMS Mathematics

2022, Volume 7, Issue 9: 16147-16170. doi: 10.3934/math.2022883

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Determine unknown source problem for time fractional pseudo-parabolic equation with Atangana-Baleanu Caputo fractional derivative

1.
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam
2.
Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam
3.
Faculty of Applied Technology, School of Engineering and Technology, Van Lang University, Ho Chi Minh City, Vietnam
4.
Department of Mathematics, University of Rajasthan, Jaipur-302004, India
5.
Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

Received: 13 May 2022 Revised: 20 June 2022 Accepted: 22 June 2022 Published: 01 July 2022
MSC : 26A33, 35B05, 35B65, 35R11

In this paper, we consider a pseudo-parabolic equation with the Atangana-Baleanu Caputo fractional derivative. Our main tool here is using fundamental tools, namely the Fractional Tikhonov method and the generalized Tikhonov method, the error estimate is shown. Finally, we provided numerical experiments to prove the correctness of our theory.
- Caputo derivative,
- pseudo-parabolic equation,
- well-posedness,
- regularity estimates
Citation: Nguyen Duc Phuong, Le Dinh Long, Devender Kumar, Ho Duy Binh. Determine unknown source problem for time fractional pseudo-parabolic equation with Atangana-Baleanu Caputo fractional derivative[J]. AIMS Mathematics, 2022, 7(9): 16147-16170. doi: 10.3934/math.2022883

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Abstract

In this paper, we consider a pseudo-parabolic equation with the Atangana-Baleanu Caputo fractional derivative. Our main tool here is using fundamental tools, namely the Fractional Tikhonov method and the generalized Tikhonov method, the error estimate is shown. Finally, we provided numerical experiments to prove the correctness of our theory.

References

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