Araştırma Makalesi

Regularization method for the problem of determining the source function using integral conditions

Cilt: 5 Sayı: 3 30 Eylül 2021
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Regularization method for the problem of determining the source function using integral conditions

Öz

In this article, we deal with the inverse problem of identifying the unknown source of the time-fractional diffusion equation in a cylinder equation by A fractional Landweber method. This problem is ill-posed. Therefore, the regularization is required. The main result of this article is the error between the sought solution and its regularized under the selection of a priori parameter choice rule.

Anahtar Kelimeler

Kaynakça

  1. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Vol. 198 of Mathematics in Science and Engineering. Academic Press: San Diego, Calif, USA, 1990.
  2. F. Mainardi, Fractional diffusive waves in viscoelastic solids Nonlinear Waves in Solids, ed J L Wegner and F R Norwood (Fairfield, NJ: ASME/AMR), pp 93--7.
  3. R.R. Nigmatullin, The realization of the generalized transfer equation in a medium with fractal geometry, Phys. Stat. Sol. B 133 (1986) 425--430.
  4. R. Metzler, J. Klafter, Boundary value problems for fractional diffusion equations, Phys. A 278 (2000) 107-125.
  5. T. Wei, Y. Zhang, The backward problem for a time-fractional diffusion- wave equation in a bounded domain, Comput. Math. Appl. 75 (2018), no. 10, 3632--3648.
  6. T. Wei, J. Xian, Variational method for a backward problem for a time-fractional diffusion equation, ESAIM Math. Model. Numer. Anal. 53 (2019), no. 4, 1223--1244.
  7. J. Xian, T. Wei, Determination of the initial data in a time-fractional diffusion-wave problem by a final time data, Comput. Math. Appl. 78 (2019), no. 8, 2525--2540.
  8. T. Wei, J.G. Wang, A modified quasi-boundary value method for the backward time-fractional diffusion problem, ESAIM Math. Model. Numer. Anal. 48 (2014), no. 2, 603--621.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

30 Eylül 2021

Gönderilme Tarihi

23 Kasım 2020

Kabul Tarihi

5 Mayıs 2021

Yayımlandığı Sayı

Yıl 2021 Cilt: 5 Sayı: 3

Kaynak Göster

APA
Nghia, B., Luc, N., Binh, H., & Long, L. D. (2021). Regularization method for the problem of determining the source function using integral conditions. Advances in the Theory of Nonlinear Analysis and its Application, 5(3), 351-361. https://doi.org/10.31197/atnaa.933212
AMA
1.Nghia B, Luc N, Binh H, Long LD. Regularization method for the problem of determining the source function using integral conditions. ATNAA. 2021;5(3):351-361. doi:10.31197/atnaa.933212
Chicago
Nghia, Bui, Nguyen Luc, Ho Binh, ve Le Dinh Long. 2021. “Regularization method for the problem of determining the source function using integral conditions”. Advances in the Theory of Nonlinear Analysis and its Application 5 (3): 351-61. https://doi.org/10.31197/atnaa.933212.
EndNote
Nghia B, Luc N, Binh H, Long LD (01 Eylül 2021) Regularization method for the problem of determining the source function using integral conditions. Advances in the Theory of Nonlinear Analysis and its Application 5 3 351–361.
IEEE
[1]B. Nghia, N. Luc, H. Binh, ve L. D. Long, “Regularization method for the problem of determining the source function using integral conditions”, ATNAA, c. 5, sy 3, ss. 351–361, Eyl. 2021, doi: 10.31197/atnaa.933212.
ISNAD
Nghia, Bui - Luc, Nguyen - Binh, Ho - Long, Le Dinh. “Regularization method for the problem of determining the source function using integral conditions”. Advances in the Theory of Nonlinear Analysis and its Application 5/3 (01 Eylül 2021): 351-361. https://doi.org/10.31197/atnaa.933212.
JAMA
1.Nghia B, Luc N, Binh H, Long LD. Regularization method for the problem of determining the source function using integral conditions. ATNAA. 2021;5:351–361.
MLA
Nghia, Bui, vd. “Regularization method for the problem of determining the source function using integral conditions”. Advances in the Theory of Nonlinear Analysis and its Application, c. 5, sy 3, Eylül 2021, ss. 351-6, doi:10.31197/atnaa.933212.
Vancouver
1.Bui Nghia, Nguyen Luc, Ho Binh, Le Dinh Long. Regularization method for the problem of determining the source function using integral conditions. ATNAA. 01 Eylül 2021;5(3):351-6. doi:10.31197/atnaa.933212

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