IDENTIFYING THE INITIAL CONDITION FOR SPACE-FRACTIONAL SOBOLEV EQUATION

Nguyen Hoang Luc; Le Dinh Long; Hang Le Thi Diem; Dumitru Baleanu; Nguyen Huu Can

doi:10.11948/20200404

2021 Volume 11 Issue 5

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Nguyen Hoang Luc, Le Dinh Long, Hang Le Thi Diem, Dumitru Baleanu, Nguyen Huu Can. IDENTIFYING THE INITIAL CONDITION FOR SPACE-FRACTIONAL SOBOLEV EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2402-2422. doi: 10.11948/20200404

Citation:

Nguyen Hoang Luc, Le Dinh Long, Hang Le Thi Diem, Dumitru Baleanu, Nguyen Huu Can. IDENTIFYING THE INITIAL CONDITION FOR SPACE-FRACTIONAL SOBOLEV EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2402-2422. doi: 10.11948/20200404

IDENTIFYING THE INITIAL CONDITION FOR SPACE-FRACTIONAL SOBOLEV EQUATION

1.
Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, 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.
Department of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
5.
Department of Mathematics, Cankaya University, Ankara, Turkey
6.
Institute of Space Sciences, Magurele–Bucharest, Romania
7.
Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Corresponding author: Email: nguyenhuucan@tdtu.edu.vn (N. H. Can)

Abstract

Abstract

In this work, a final value problem for a fractional pseudo-parabolic equation is considered. Firstly, we present the regularity of solution. Secondly, we show that this problem is ill-posed in Hadamard's sense. After that we use the quasi–boundary value regularization method to solve this problem. To show that the proposed theoretical results are appropriate, we present an illustrative numerical example.
- Final value problem /
- fractional pseudo-parabolic equation /
- Illposed problem /
- convergence estimates /
- regularization
MSC: 35K05, 35K99, 47J06, 47H10x

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References

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