Research Article

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

Volume: 5 Number: 3 September 30, 2022
EN

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

Supporting Institution

FPT University HCM

References

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  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.
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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

September 30, 2022

Submission Date

July 17, 2022

Acceptance Date

August 19, 2022

Published in Issue

Year 2022 Volume: 5 Number: 3

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 (September 1, 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, vol. 5, no. 3, pp. 387–392, Sept. 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 (September 1, 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, vol. 5, no. 3, Sept. 2022, pp. 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. 2022 Sep. 1;5(3):387-92. doi:10.53006/rna.1144709

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