BibTex RIS Kaynak Göster

Nonhomogeneous Generalized Multi-Term Fractional Heat Propagation and Fractional Diffusion-Convection Equation in Three-Dimensional Space

Yıl 2014, Cilt: 2 Sayı: 2, 106 - 116, 01.08.2014

Öz

The main purpose of this article is to study non-homogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three-dimensional space, where the fractional derivative is defined in the Caputo sense. The convection-diffusion equation describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection

Kaynakça

  • Aghili A., Masomi M.R. Solution to time fractional partial differential equations and dynamical systems via integral transform. Journal of Interdisciplinary Mathematics ( Taru Publications) . Vol.14 (2011),No.5&6,pp.545-560.
  • Aghili A. Masomi M.R. Solution to time fractional partial differential equations via joint Laplace – Fourier transform. Journal of Interdisciplinary Mathematics ( Taru Publications) . Vol.15 (2012),No.2&3,pp.121-135.
  • Jiang H., Liu F., Turner I., and Burrage K. Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. J. Math. Anal. Appl. 389 (2012) 1117-1127.
  • Jiang H., Liu F., Turner I., and Burrage K. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion in a finite domain. Computers &Mathematics with Applications (March 2012). doi:10.1016/j.camwa.2012.02.042
  • Zhang F., Jiang X. Analytical solutions for a time-fractional axisymmetric diffusion-wave equation with a source term. Nonlinear Analysis: Real World Applications 12 (2011) 1841–1849.
  • Debnath L. Fractional integral and fractional differential equations in fluid mechanics. Fract. Calc. Appl. Anal. 6 (2003) 119–55.
  • Nikolova Y., and Boyadjiev L. Integral transforms method to solve a time-space fractional diffusion equation Fract. Calc. Appl. Anal. 13 (2010) 57–67.
  • Saxena R.K., Mathai A.M., and Haubold H.J. Fractional reaction-diffusion equations Astrophys. Space Sci. 305 (2006) 289–96.
  • Saxena R.K., Mathai A.M., and Haubold H.J. Solution of generalized fractional reaction-diffusion equations Astrophys. Space Sci. 305 (2006) 305–13.
  • Ditkin, V.A, Prudnikov. A.P. Calcul operationnel. Edition de Moscow, 1979.

Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space

Yıl 2014, Cilt: 2 Sayı: 2, 106 - 116, 01.08.2014

Öz

Kaynakça

  • Aghili A., Masomi M.R. Solution to time fractional partial differential equations and dynamical systems via integral transform. Journal of Interdisciplinary Mathematics ( Taru Publications) . Vol.14 (2011),No.5&6,pp.545-560.
  • Aghili A. Masomi M.R. Solution to time fractional partial differential equations via joint Laplace – Fourier transform. Journal of Interdisciplinary Mathematics ( Taru Publications) . Vol.15 (2012),No.2&3,pp.121-135.
  • Jiang H., Liu F., Turner I., and Burrage K. Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. J. Math. Anal. Appl. 389 (2012) 1117-1127.
  • Jiang H., Liu F., Turner I., and Burrage K. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion in a finite domain. Computers &Mathematics with Applications (March 2012). doi:10.1016/j.camwa.2012.02.042
  • Zhang F., Jiang X. Analytical solutions for a time-fractional axisymmetric diffusion-wave equation with a source term. Nonlinear Analysis: Real World Applications 12 (2011) 1841–1849.
  • Debnath L. Fractional integral and fractional differential equations in fluid mechanics. Fract. Calc. Appl. Anal. 6 (2003) 119–55.
  • Nikolova Y., and Boyadjiev L. Integral transforms method to solve a time-space fractional diffusion equation Fract. Calc. Appl. Anal. 13 (2010) 57–67.
  • Saxena R.K., Mathai A.M., and Haubold H.J. Fractional reaction-diffusion equations Astrophys. Space Sci. 305 (2006) 289–96.
  • Saxena R.K., Mathai A.M., and Haubold H.J. Solution of generalized fractional reaction-diffusion equations Astrophys. Space Sci. 305 (2006) 305–13.
  • Ditkin, V.A, Prudnikov. A.P. Calcul operationnel. Edition de Moscow, 1979.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

Arman Aghili Bu kişi benim

Mohamed Rasool Masomi Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 2 Sayı: 2

Kaynak Göster

APA Aghili, A., & Masomi, M. . R. (2014). Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space. New Trends in Mathematical Sciences, 2(2), 106-116.
AMA Aghili A, Masomi MR. Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space. New Trends in Mathematical Sciences. Ağustos 2014;2(2):106-116.
Chicago Aghili, Arman, ve Mohamed Rasool Masomi. “Nonhomogeneous Generalized Multi-Term Fractional Heat Propagation and Fractional Diffusion-Convection Equation in Three- Dimensional Space”. New Trends in Mathematical Sciences 2, sy. 2 (Ağustos 2014): 106-16.
EndNote Aghili A, Masomi MR (01 Ağustos 2014) Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space. New Trends in Mathematical Sciences 2 2 106–116.
IEEE A. Aghili ve M. . R. Masomi, “Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space”, New Trends in Mathematical Sciences, c. 2, sy. 2, ss. 106–116, 2014.
ISNAD Aghili, Arman - Masomi, Mohamed Rasool. “Nonhomogeneous Generalized Multi-Term Fractional Heat Propagation and Fractional Diffusion-Convection Equation in Three- Dimensional Space”. New Trends in Mathematical Sciences 2/2 (Ağustos 2014), 106-116.
JAMA Aghili A, Masomi MR. Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space. New Trends in Mathematical Sciences. 2014;2:106–116.
MLA Aghili, Arman ve Mohamed Rasool Masomi. “Nonhomogeneous Generalized Multi-Term Fractional Heat Propagation and Fractional Diffusion-Convection Equation in Three- Dimensional Space”. New Trends in Mathematical Sciences, c. 2, sy. 2, 2014, ss. 106-1.
Vancouver Aghili A, Masomi MR. Nonhomogeneous generalized multi-term fractional heat propagation and fractional diffusion-convection equation in three- dimensional space. New Trends in Mathematical Sciences. 2014;2(2):106-1.