Fractional diffusion equation in half-space with Robin boundary condition

• Authors: Jun-Sheng Duan , Zhong Wang , Shou-Zhong Fu
• Languages of publication: EN

Abstracts

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.

Keywords

EN

fractional calculus; Laplace transform; fractional diffusion equation; Mittag-Leffler function; integral transform

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 6
• Pages: 799-805

Dates

published

1 - 6 - 2013

online

9 - 10 - 2013

Contributors

author

Jun-Sheng Duan

author

Zhong Wang

• School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China

author

Shou-Zhong Fu

• School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China

References

• [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]
• [11] H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Rom. Rep. Phys. 64, 337 (2012)
• [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]

Identifiers

DOI

10.2478/s11534-013-0206-4