Results for a fractional diffusion equation with a nonlocal term in spherical symmetry

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 372, Issue 40, 2008, Pages 6121-6124

  Lenzi, E K ^a   Lenzi, M K ^b   Rossato, R ^a   Evangelista, L R ^a   da Silva, L R ^c  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^c FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

Author keywords

Anomalous diffusion; Fractional diffusion equation

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS;

ANOMALOUS DIFFUSION; DIFFUSION EQUATIONS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFUSION EQUATION; NONLOCAL TERM; SPHERICAL SYMMETRY; TIME EVOLUTIONS; TIME-DEPENDENT SOLUTIONS;

DIFFUSION;

EID: 51349156106     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2008.08.029     Document Type: Article

References (47)

1. Hilfer R., Metzler R., Blumen A., and Klafter J. Strange Kinetics. Chemical Physics vol. 284 (2004), Pergamon-Elsevier, Amsterdam Numbers 1-2
2. Hilfer R. Applications of Fractional Calculus in Physics (2000), World Scientific, Singapore
3. Metzler R., and Klafter J. Phys. Rep. 339 (2000) 1
4. Heinsalu E., Patriarca M., Goychuk I., and Hänggi P. Phys. Rev. Lett. 99 (2007) 120602
5. Kosztolowicz T., Dworecki K., and Mrowczynski St. Phys. Rev. Lett. 94 (2005) 170602
6. Uchaikin V.V., and Sibatov R.T. Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 715
7. Valdes-Parada F.J., Ochoa-Tapia J.A., and Alvarez-Ramirez J. Physica A 373 (2007) 339
8. Chukbar K., and Zaburdaev V. Phys. Rev. E 71 (2005) 061105
9. Iomin A. J. Phys.: Conf. Ser. 7 (2005) 57
10. Iomin A. Phys. Rev. E 73 (2006) 061918
11. Fedotov S., and Iomin A. Phys. Rev. Lett. 98 (2007) 118101
12. Metzler R., Barkai E., and Klafter J. Europhys. Lett. 46 (1999) 431
13. Ryabov Y.E. Phys. Rev. E 68 (2003) 030102R
14. Kalmykov Y.P., Coffey W.T., and Titov S.V. Phys. Rev. E 75 (2007) 031101
15. Seki K., Wojcik M., and Tachiya M. J. Chem. Phys. 119 (2003) 2165
16. Yuste S.B., Acedo L., and Lindenberg K. Phys. Rev. E 69 (2004) 036126
17. Sokolov I.M., Schmidt M.G.W., and Sagués F. Phys. Rev. E 73 (2006) 031102
18. Srokowski T. Phys. Rev. E 75 (2007) 051105
19. Krepysheva N., Di Pietro L., and Neel M.C. Phys. Rev. E 73 (2006) 021104
20. Achar B.N.N., and Hanneken J.W. J. Mol. Liq. 114 (2004) 147
21. Ren F.-Y., Liang J.-R., Qiu W.-Y., Wang X.-T., Xu Y., and Nigmatullin R.R. Phys. Lett. A 312 (2003) 187
22. Agrawal O.M.P. Nonlinear Dynam. 29 (2002) 145
23. Hanyga A. Proc. R. Soc. London A 458 (2002) 429
24. El-Wakil S.A., Elhanbaly A., and Zahran M.A. Chaos Solitons Fractals 12 (2001) 1035
25. Lenzi E.K., Mendes R.S., Fa K.S., Malacarne L.C., and da Silva L.R. J. Math. Phys. 44 (2003) 2179
26. Lenzi E.K., Mendes R.S., Andrade J.S., da Silva L.R., and Lucena L.S. Phys. Rev. E 71 (2005) 052109
27. Assis da Silva P.C., de Souza R.P., da Silva P.C., da Silva L.R., Lucena L.S., and Lenzi E.K. Phys. Rev. E 73 (2006) 032101
28. Murray J.D. Mathematical Biolog. I. An Introduction (2001), Heidelberg, Springer
29. Balescu R. Phys. Rev. E 51 (1995) 4807
30. Macheras P., and Iliadis A. Modeling in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics (2006), Springer, New York
31. Ben-Avraham D., and Havlin S. Diffusion and Reactions in Fractals and Disordered Systems (2000), Cambridge Univ. Press, New York
32. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
33. Latora V., Rapisarda A., and Ruffo S. Phys. Rev. Lett. 83 (1999) 2104
34. Latora V., Rapisarda A., and Tsallis C. Phys. Rev. E 64 (2001) 056134
35. Caspi A., Granek R., and Elbaum M. Phys. Rev. Lett. 85 (2000) 5655
36. Caspi A., Granek R., and Elbaum M. Phys. Rev. E 66 (2002) 011916
37. Henry B.I., Langlands T.A.M., and Wearne S.L. Phys. Rev. E 74 (2006) 031116
38. Schot A., Lenzi M.K., Evangelista L.R., Malacarne L.C., Mendes R.S., and Lenzi E.K. Phys. Lett. A 366 (2007) 346
39. Morse M.P., and Feshbach H. Methods of Theoretical Physics (1953), McGraw-Hill, New York
40. Mathai A.M., and Saxena R.K. The H-Function with Application in Statistics and other Disciplines (1978), Wiley Eastern, New Delhi
41. Lenzi E.K., Oliveira B.F., da Silva L.R., and Evangelista L.R. J. Math. Phys. 49 (2008) 032108
42. Ryabov Y.E. Phys. Rev. E 68 (2003) 030102R
43. Malacarne L.C., Mendes R.S., Lenzi E.K., and Lenzi M.K. Phys. Rev. E 74 (2006) 042101
44. Chechkin A.V., Gorenflo R., and Sokolov I.M. Phys. Rev. E 66 (2002) 046129
45. Sokolov I.M., Chechkin A.V., and Klafter J. Acta Phys. Pol. B 35 (2004) 1323
46. Mainardi F., and Pagnini G. J. Comput. Appl. Math. 207 (2007) 245
47. Sokolov I.M., Chechkin A.V., and Klafter J. Physica A 336 (2004) 245