Araştırma Makalesi
BibTex RIS Kaynak Göster

Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions

Yıl 2023, Cilt: 11 Sayı: 2, 148 - 154, 31.10.2023

Süleyman Çetinkaya Ali Demir

Öz

In this research, we discuss the construction of analytic solution of homogenous initial boundary value problem including PDEs of fractional order. Since homogenous initial boundary value problem involves local fractional order derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on $L^2\left[0,l\right]$, the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem including fractional derivative in local sense used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.

Anahtar Kelimeler

Local Fractional Derivative Dirichlet boundary conditions Spectral method Separation of variables

Kaynakça

  • [1] D. Baleanu, A. Fernandez, A. Akg¨ul, On a Fractional Operator Combining Proportional and Classical Differintegrals, Mathematics Vol. 8, No. 360 (2020).
  • [2] J. Bisquert, Interpretation of a fractional diffusion equation with nonconserved probability density in terms of experimental systems with trapping or recombination, Physical Review E Vol. 72, (2005), 011109.
  • [3] N. Sene, Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model, International Journal of Analysis and Applications Vol. 17, No. 2 (2019), 191–207.
  • [4] J. F. G. Aguilar, M. M. Hernandez, Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative, Abstract and Applied Analysis, Vol. 2014, (2014), Article ID 283019.
  • [5] M. Naber, Distributed order fractional sub-diffusion, Fractals Vol. 12, No. 1 (2004), 23–32.
  • [6] E. Nadal, E. Abisset-Chavanne, E. Cueto, F. Chinesta, On the physical interpretation of fractional diffusion, Comptes Rendus Mecanique, Vol. 346 (2018), 581-589.
  • [7] W. Zhang and M. Yi, Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals, Advances in Difference Equations Vol. 2016, No. 217 (2016).

Yıl 2023, Cilt: 11 Sayı: 2, 148 - 154, 31.10.2023

Süleyman Çetinkaya Ali Demir

Öz

Kaynakça

  • [1] D. Baleanu, A. Fernandez, A. Akg¨ul, On a Fractional Operator Combining Proportional and Classical Differintegrals, Mathematics Vol. 8, No. 360 (2020).
  • [2] J. Bisquert, Interpretation of a fractional diffusion equation with nonconserved probability density in terms of experimental systems with trapping or recombination, Physical Review E Vol. 72, (2005), 011109.
  • [3] N. Sene, Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model, International Journal of Analysis and Applications Vol. 17, No. 2 (2019), 191–207.
  • [4] J. F. G. Aguilar, M. M. Hernandez, Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative, Abstract and Applied Analysis, Vol. 2014, (2014), Article ID 283019.
  • [5] M. Naber, Distributed order fractional sub-diffusion, Fractals Vol. 12, No. 1 (2004), 23–32.
  • [6] E. Nadal, E. Abisset-Chavanne, E. Cueto, F. Chinesta, On the physical interpretation of fractional diffusion, Comptes Rendus Mecanique, Vol. 346 (2018), 581-589.
  • [7] W. Zhang and M. Yi, Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals, Advances in Difference Equations Vol. 2016, No. 217 (2016).
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Articles
Yazarlar

Süleyman Çetinkaya

Ali Demir

Yayımlanma Tarihi 31 Ekim 2023
Gönderilme Tarihi 21 Ekim 2020
Kabul Tarihi 5 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 11 Sayı: 2

Kaynak Göster

APA Çetinkaya, S., & Demir, A. (2023). Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions. Konuralp Journal of Mathematics, 11(2), 148-154.
AMA Çetinkaya S, Demir A. Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions. Konuralp J. Math. Ekim 2023;11(2):148-154.
Chicago Çetinkaya, Süleyman, ve Ali Demir. “Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions”. Konuralp Journal of Mathematics 11, sy. 2 (Ekim 2023): 148-54.
EndNote Çetinkaya S, Demir A (01 Ekim 2023) Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions. Konuralp Journal of Mathematics 11 2 148–154.
IEEE S. Çetinkaya ve A. Demir, “Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions”, Konuralp J. Math., c. 11, sy. 2, ss. 148–154, 2023.
ISNAD Çetinkaya, Süleyman - Demir, Ali. “Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions”. Konuralp Journal of Mathematics 11/2 (Ekim 2023), 148-154.
JAMA Çetinkaya S, Demir A. Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions. Konuralp J. Math. 2023;11:148–154.
MLA Çetinkaya, Süleyman ve Ali Demir. “Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions”. Konuralp Journal of Mathematics, c. 11, sy. 2, 2023, ss. 148-54.
Vancouver Çetinkaya S, Demir A. Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions. Konuralp J. Math. 2023;11(2):148-54.
 Kapak Resmi İndir
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.