On terminal value problem for fractional superdiffusive of Sobolev equation type

Bui Duc Nam; Le Nhat Huynh; Le Dinh Long; Yusuf Gurefe

doi:10.3934/dcdss.2023172

Article Contents

2024, Volume 17, Issue 3: 1195-1207. Doi: 10.3934/dcdss.2023172

This issue Previous Article Regularity and convergent result of mild solution of Love equation Next Article On the integro-differential equation with conformable derivative

On terminal value problem for fractional superdiffusive of Sobolev equation type

1.
Ho Chi Minh City University of Industry and Trade, Ho Chi Minh City, Vietnam
2.
Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam
3.
Vietnam National University, Ho Chi Minh City, Vietnam
4.
Faculty of Maths, FPT University HCM, Saigon Hi-tech Park, Ho Chi Minh City, Vietnam
5.
Department of Mathematics, Faculty of Science, Mersin University, Mersin, Turkey

^*Corresponding author: Yusuf Gurefe (yusufgurefe@mersin.edu.tr). E-mail of other authors: nambd@hufi.edu.vn (Bui Duc Nam), lenhathuynh@gmail.com (Le Nhat Huynh), longld13@fe.edu.vn (Le Dinh Long)
^*Corresponding author: Yusuf Gurefe (yusufgurefe@mersin.edu.tr). E-mail of other authors: nambd@hufi.edu.vn (Bui Duc Nam), lenhathuynh@gmail.com (Le Nhat Huynh), longld13@fe.edu.vn (Le Dinh Long)

Document Type: Research Article.

Received: May 2023

Revised: July 2023

Early access: September 15, 2023

Published online: September 15, 2023

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Abstract

In this paper, we consider the terminal value problem for fractional super diffusive equation in case linear source function. This equation has many applications in physical phenomena. The results in this study are mainly provide the existence and regularity of the mild solution under the various assumptions of the input data.

Keywords:

Fractional nonclassical diffusion equation,
well–posedness,
ill-posedness,
regularity estimates,
regularization and error estimate.

Mathematics Subject Classification: 26A33, 35B65, 35R11.

Citation:

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References

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