Araştırma Makalesi

Note on the convergence of fractional conformable diffusion equation with linear source term

Cilt: 5 Sayı: 3 30 Eylül 2022
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Note on the convergence of fractional conformable diffusion equation with linear source term

Abstract

In this paper, we study the diffusion equation with conformable derivative. The main goal is to prove the convergence of the mild solution to our problem when the order of fractional Laplacian tends to $1^-$. The principal techniques of our paper is based on some useful evaluations for exponential kernels.

Keywords

Destekleyen Kurum

FPT University HCM

Kaynakça

  1. [1] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70.
  2. [2] A.A. Abdelhakim, J.A. T. Machado, A critical analysis of the conformable derivative, Nonlinear Dynamics, Volume 95, Issue 4, (2019), 3063–3073.
  3. [3] W.S. Chung, Fractional Newton mechanics with conformable fractional derivative, Journal of Computational and Applied Mathematics, Volume 290 (2015), Pages 150–158.
  4. [4] A. Jaiswal, D. Bahuguna, Semilinear Conformable Fractional Differential Equations in Banach Spaces, Differ. Equ. Dyn. Syst. 27 , no. 1-3, (2019), 313–325.
  5. [5] V.F. Morales-Delgado, J.F. Gómez-Aguilar, R.F. Escobar-Jiménez, M.A. Taneco-Hernández, Fractional conformable derivatives of Liouville-Caputo type with low-fractionality, Physica A: Statistical Mechanics and its Applications, Volume 503 (2018), 424–438.
  6. [6] S. He, K. Sun, X. Mei, B. Yan, S. Xu, Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative, Eur. Phys. J. Plus, (2017) 132: 36. https://doi.org/10.1140/epjp/i2017-11306-3.
  7. [7] F.M. Alharbi, D. Baleanu, A. Ebaid, Physical properties of the projectile motion using the conformable derivative, Chinese Journal of Physics, Volume 58, (2019), Pages 18–28.
  8. [8] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57–66.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

30 Eylül 2022

Gönderilme Tarihi

17 Temmuz 2022

Kabul Tarihi

19 Ağustos 2022

Yayımlandığı Sayı

Yıl 2022 Cilt: 5 Sayı: 3

Kaynak Göster

APA
Nguyen, T. (2022). Note on the convergence of fractional conformable diffusion equation with linear source term. Results in Nonlinear Analysis, 5(3), 387-392. https://doi.org/10.53006/rna.1144709
AMA
1.Nguyen T. Note on the convergence of fractional conformable diffusion equation with linear source term. RNA. 2022;5(3):387-392. doi:10.53006/rna.1144709
Chicago
Nguyen, Tien. 2022. “Note on the convergence of fractional conformable diffusion equation with linear source term”. Results in Nonlinear Analysis 5 (3): 387-92. https://doi.org/10.53006/rna.1144709.
EndNote
Nguyen T (01 Eylül 2022) Note on the convergence of fractional conformable diffusion equation with linear source term. Results in Nonlinear Analysis 5 3 387–392.
IEEE
[1]T. Nguyen, “Note on the convergence of fractional conformable diffusion equation with linear source term”, RNA, c. 5, sy 3, ss. 387–392, Eyl. 2022, doi: 10.53006/rna.1144709.
ISNAD
Nguyen, Tien. “Note on the convergence of fractional conformable diffusion equation with linear source term”. Results in Nonlinear Analysis 5/3 (01 Eylül 2022): 387-392. https://doi.org/10.53006/rna.1144709.
JAMA
1.Nguyen T. Note on the convergence of fractional conformable diffusion equation with linear source term. RNA. 2022;5:387–392.
MLA
Nguyen, Tien. “Note on the convergence of fractional conformable diffusion equation with linear source term”. Results in Nonlinear Analysis, c. 5, sy 3, Eylül 2022, ss. 387-92, doi:10.53006/rna.1144709.
Vancouver
1.Tien Nguyen. Note on the convergence of fractional conformable diffusion equation with linear source term. RNA. 01 Eylül 2022;5(3):387-92. doi:10.53006/rna.1144709

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