Time-fractional radial diffusion in hollow geometries

Meccanica

Volumn 45, Issue 4, 2010, Pages 577-583

  Qi, Haitao ^a   Liu, Jiaguo ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Analytical solutions; Anomalous diffusion; Caputo fractional derivative; Mittag Leffler functions

Indexed keywords

ANALYTICAL SOLUTIONS; ANOMALOUS DIFFUSION; CAPUTO FRACTIONAL DERIVATIVES; METHOD OF SEPARATIONS; MITTAG-LEFFLER FUNCTIONS; NUMERICAL RESULTS; RADIAL DIFFUSION; SIMILAR SOLUTION;

FUNCTIONS; LAPLACE TRANSFORMS; NUMERICAL ANALYSIS; WAVE EQUATIONS;

DIFFUSION;

EID: 77955658476     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11012-009-9275-2     Document Type: Article

References (38)

1. R Metzler J Klafter 2000 The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys Rep 339 1 77 0984.82032 10.1016/S0370- 1573(00)00070-3 1809268 2000PhR...339....1M
2. GM Zaslavsky 2002 Chaos, fractional kinetics, and anomalous transport Phys Rep 371 461 580 0999.82053 10.1016/S0370-1573(02)00331-9 1937584 2002PhR...371..461Z
3. JW Hanneken BN Narahari Achar DM Vaught, et al. 2004 A random walk simulation of fractional diffusion J Mol Liq 114 153 157 10.1016/j.molliq.2004. 02.013
4. R Metzler J Klafter 2004 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J Phys A 37 161 208 10.1088/0305-4470/37/31/R01 2090004 2004JPhA...37R.161M (Pubitemid 39063557)
5. IM Sokolov J Klafter 2005 From diffusion to anomalous diffusion: A century after Einstein's Brownian motion Chaos 15 026103 10.1063/1.1860472 2150232 2005Chaos..15b6103S (Pubitemid 43127627)
6. MY Xu WC Tan 2006 Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics Sci China Ser G 49 257 272 1109.26005 10.1007/s11433-006-0257-2
7. R Gorenflo F Mainardi 2009 Some recent advances in theory and simulation of fractional diffusion process J Comput Appl Math 229 400 415 1166.45004 10.1016/j.cam.2008.04.005 2527894 2009JCoAm.229..400G
8. XY Jiang MY Xu 2009 The fractional finite Hankel transform and its applications in fractal space J Phys A, Math Theor 42 385201 10.1088/1751-8113/42/38/385201 2540388 2009JPhA...42L5201J
9. JM Sancho AM Lacasta K Lindenberg, et al. 2004 Diffusion on a solid surface: Anomalous is normal Phys Rev Lett 92 250601 10.1103/PhysRevLett.92. 250601 2004PhRvL..92y0601S
10. J Klafter IM Sokolov 2005 Anomalous diffusion spreads its wings Phys World 18 29 32
11. WC Tan CQ Fu CJ Fu, et al. 2007 An anomalous subdiffusion model for calcium spark in cardiac myocytes Appl Phys Lett 91 183901 10.1063/1.2805208 2007ApPhL..91r3901T (Pubitemid 350037255)
12. Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
13. Hilfer R (2000) Applications of fractional calculus in physics. World Scientific, Singapore
14. AMA El-Sayed 1996 Fractional order diffusion-wave equation Int J Theor Phys 35 311 322 0846.35001 10.1007/BF02083817 1372176
15. A Hanyga 2002 Multidimensional solutions of space-time-fractional diffusion equation Proc R Soc Lond A 458 429 450 0999.60035 10.1098/rspa.2001. 0893 1889936 2002RSPSA.458..429H
16. SD Eidelman AN Kochubei 2004 Cauchy problem for fractional diffusion equation J Differ Equ 199 211 255 1068.35037 10.1016/j.jde.2003.12.002 2047909 (Pubitemid 38516155)
17. W Wyss 1986 The fractional diffusion equation J Math Phys 27 2782 2785 0632.35031 10.1063/1.527251 861345 1986JMP....27.2782W
18. WR Schneider W Wyss 1989 Fractional diffusion and wave equations J Math Phys 30 134 144 0692.45004 10.1063/1.528578 974464 1989JMP....30..134S
19. R Gorenflo Y Luchko F Mainardi 2000 Wright function as scale-invariant solutions of the diffusion-wave equation J Comput Appl Math 118 175 191 0973.35012 10.1016/S0377-0427(00)00288-0 1765948
20. OP Agrawal 2001 A general solution for a fourth-order fractional diffusion-wave equation defined in a bounded domain Comput Struct 79 1497 1501 10.1016/S0045-7949(01)00026-8 (Pubitemid 32724603)
21. OP Agrawal 2002 Solution for a fractional diffusion-wave equation defined in a bounded domain Nonlinear Dyn 29 145 155 1009.65085 10.1023/A:1016539022492 (Pubitemid 34945396)
22. OP Agrawal 2003 Response of a diffusion-wave system subjected to deterministic and stochastic fields Z Angew Math Mech 83 265 274 1045.35116 10.1002/zamm.200310033
23. BN Narahari Achar JW Hanneken 2004 Fractional radial diffusion in a cylinder J Mol Liq 114 147 151 10.1016/j.molliq.2004.02.012
24. YZ Povstenko 2007 Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation Int J Solids Struct 44 2324 2348 1121.74022 10.1016/j.ijsolstr.2006.07.008 2295355
25. YZ Povstenko 2008 Time-fractional radial diffusion in a sphere Nonlinear Dyn 53 55 65 1170.76357 10.1007/s11071-007-9295-1 2411428
26. YZ Povstenko 2008 Fractional radial diffusion in a cylinder J Mol Liq 137 46 50 10.1016/j.molliq.2007.03.006 (Pubitemid 350180103)
27. YZ Povstenko 2008 Fundamental solutions to three-dimensional diffusion-wave equation and associated diffusive stresses Chaos, Solitons and Fractals 36 961 972 1131.74022 10.1016/j.chaos.2006.07.031 2379364
28. YZ Povstenko 2008 Fractional heat conduction equation and associated thermal stresses in an infinite solid with spherical cavity Q J Mech Appl Math 61 523 547 1153.74012 10.1093/qjmam/hbn016 2448643
29. YZ Povstenko 2009 Fractional radial diffusion in an infinite medium with a cylindrical cavity Q Appl Math 67 113 123 1165.26303 2495074
30. N Özdemir D Karadeniz 2008 Fractional diffusion-wave problem in cylindrical coordinates Phys Lett A 372 5968 5972 10.1016/j.physleta.2008.07.054 2458899 2008PhLA..372.5968O
31. Korenev BG (2002) Bessel functions and their applications. Taylor & Francis, London
32. Crank J (1975) The mathematics of diffusion, 2nd edn. Clarendon, Oxford
33. YP Lü M Bülow 2000 Analysis of diffusion in hollow geometries Adsorption 6 125 136 10.1023/A:1008913301145
34. IB Huang SK Yen 2002 Diffusion in hollow cylinders for some boundary conditions I. Mathematical treatment Mater Chem Phys 74 289 299 10.1016/S0254-0584(01)00483-7 (Pubitemid 34154079)
35. Debnath L, Bhatta D (2007) Integral transforms and their applications, 2nd edn. Chapman & Hall/CRC Press, Boca Raton
36. HT Qi H Jin 2009 Unsteady helical flows of a generalized Oldroyd-B fluid with fractional derivative Nonlinear Anal: Real World Appl 10 2700 2708 1162.76006 10.1016/j.nonrwa.2008.07.008 2523233
37. DK Tong LT Shan 2009 Exact solutions for generalized Burgers fluid in an annular pipe Meccanica 44 427 431 05624227 10.1007/s11012-008-9179-6 2525015
38. S Hyder Ali Muttaqi Shah 2009 Some helical flows of a Burgers fluid with fractional derivative Meccanica 10.1007/s11012-009-9233-z