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2013 | 11 | 6 | 799-805
Tytuł artykułu

Fractional diffusion equation in half-space with Robin boundary condition

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The initial and boundary value problem for the fractional diffusion equation in half-space with the Robin boundary condition is considered. The solution is comprised of two parts: the contribution of the initial value and the contribution of the boundary value, for which the respective fundamental solutions are given. Finally, the solution formula of the considered problem is obtained.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
6
Strony
799-805
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-10-09
Twórcy
autor
  • School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China
  • School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China
Bibliografia
  • [1] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic, New York, 1974)
  • [2] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)
  • [3] F. Mainardi, In: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics (Springer-Verlag, Wien/New York, 1997) 291
  • [4] I. Podlubny, Fractional Differential Equations (Academic, San Diego, 1999)
  • [5] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006)
  • [6] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity (Imperial College, London, 2010) http://dx.doi.org/10.1142/9781848163300[Crossref]
  • [7] J. Klafter, S. C. Lim, R. Metzler, Fractional Dynamics: Recent Advances (World Scientific, Singapore, 2011) http://dx.doi.org/10.1142/8087[Crossref]
  • [8] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods (Series on Complexity, Nonlinearity and Chaos) (World Scientific, Boston, 2012)
  • [9] H. Jafari, H. Tajadodi, D. Baleanu, Fract. Calc. Appl. Anal. 16, 109 (2013)
  • [10] D. Baleanu, O. G. Mustafa, D. O’Regan, Adv. Differ. Equ. 2012, 145 (2012) http://dx.doi.org/10.1186/1687-1847-2012-145[Crossref]
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  • [12] J. S. Duan, T. Chaolu, R. Rach, Appl. Math. Comput. 218, 8370 (2012) http://dx.doi.org/10.1016/j.amc.2012.01.063[Crossref]
  • [13] J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, Commun. Frac. Calc. 3, 73 (2012)
  • [14] J. S. Duan, Z. Wang, Y. L. Liu, X. Qiu, Chaos Soliton. Fract. 46, 46 (2013) http://dx.doi.org/10.1016/j.chaos.2012.11.004[Crossref]
  • [15] M. Giona, H. E. Roman, Physica A 185, 87 (1992) http://dx.doi.org/10.1016/0378-4371(92)90441-R[Crossref]
  • [16] F. Mainardi, Appl. Math. Lett. 9, 23 (1996) http://dx.doi.org/10.1016/0893-9659(96)00089-4[Crossref]
  • [17] F. Mainardi, Chaos Soliton. Fract. 7, 1461 (1996) http://dx.doi.org/10.1016/0960-0779(95)00125-5[Crossref]
  • [18] R. R. Nigmatullin, Phys. Stat. Sol. B 133, 425 (1986) http://dx.doi.org/10.1002/pssb.2221330150[Crossref]
  • [19] R. Metzler, J. Klafter, Physica A 278, 107 (2000) http://dx.doi.org/10.1016/S0378-4371(99)00503-8[Crossref]
  • [20] J. S. Duan, J. Math. Phys. 46, 13504 (2005) http://dx.doi.org/10.1063/1.1819524[Crossref]
  • [21] B. Davies, Integral Transforms and Their Applications, 3rd edition (Springer-Verlag, New York, 2001)
  • [22] R. Gorenflo, J. Loutchko, Y. Luchko, Fract. Calc. Appl. Anal. 5, 491 (2002)
  • [23] J. Abate, P. P. Valkó, Int. J. Numer. Meth. Engng. 60, 979 (2004) http://dx.doi.org/10.1002/nme.995[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0206-4
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