Fractional reaction-diffusion equation for species ... - ResearchGate

More documents

Recommendations

Info

20 Baeumer, Kovács, Meerschaert 17. Clark,J. S., Lewis, M., Horvath, L.: Invasion by Extremes: Population Spread with Variation in Dispersal and Reproduction The American Naturalist 157(5), 537–554 (2001) 18. Cliff, M., Goldstein, J.A., Wacker, M.: Positivity, Trotter products, and blowup. Positivity 8(2), 187–208 (2004) 19. del Castillo-Negrete, D., Carreras, B.A., Lynch, V.E.: Front dynamics in reaction-diffusion systems with levy flights: A fractional diffusion approach. Physical Review Letters 91(1), 018302 (2003) 20. Engel, K.J., Nagel, R.: One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194. Springer-Verlag, New York (2000). With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt 21. Feller, W.: An Introduction to Probability Theory and Applications. Volumes I and II. John Wiley and Sons (1966) 22. Gorenflo, R., Mainardi, F., Scalas, E., Raberto, M.: Problems with using existing transport models to describe microbial transport in porous media. In: Trends Math., pp. 171–180. American Society for Microbiology, Mathematical finance (Konstanz, 2000) (2001) 23. Heyde, C.C., Leonenko, N.N.: Student Processes. Advances in Applied Probability 37, 342–365 (2005) 24. Hille, E., Phillips, R.S.: Functional analysis and semi-groups. American Mathematical Society, Providence, R. I. (1974). Third printing of the revised edition of 1957, American Mathematical Society Colloquium Publications, Vol. XXXI 25. Jacob, N.: Pseudo-differential operators and Markov processes, Mathematical Research, vol. 94. Akademie Verlag, Berlin (1996) 26. Katul, G.G., Porporato, A., Nathan, R., Siqueira, M., Soons, M.B., Poggi, D., Horn, H.S., Levin, S.A.: Mechanistic analytical models for long-distance seed dispersal by wind. The American Naturalist 166, 368–381 (2005) 27. Klafter, J., Blumen, A., Shlesinger, M.F.: Stochastic pathways to anomalous diffusion. Phys. Rev. A 35, 3081–3085 (1987) 28. Klein, E.K., Lavigne, C., Picault, H., Renard, M., Gouyon, P.H.: Pollen dispersal of oilseed rape: estimation of the dispersal function and effects of field dimension. Journal of Applied Ecology 43(10), 141–151 (2006) 29. Kozubowski, T., Meerschaert, M., Podgórski, K: Fractional Laplace Motion. Advances in Applied Probability 38(2), to appear (2006) http://www.maths. otago.ac.nz/%7Emcubed/fLaplace.pdf 30. Lockwood, D.R., Hastings, A.: The effects of dispersal patterns on marine reserves: Does the tail wag the dog Theoretical Population Biology 61, 297– 309 (2002) 31. Meerschaert, M., Mortensen, J., Wheatcraft, S.: Fractional vector calculus for fractional advection-dispersion. Physica A p. to appear (2006) 32. Meerschaert, M.M., Benson, D.A., Baeumer, B.: Multidimensional advection and fractional dispersion. Phys. Rev. E 59, 5026–5028 (1999) 33. Meerschaert, M.M., Benson, D.A., Baeumer, B.: Operator Lévy motion and multiscaling anomalous diffusion. Phys. Rev. E 63, 1112–1117 (2001) 34. Meerschaert, M.M., Benson, D.A., Scheffler, H., Baeumer, B.: Stochastic solution of space-time fractional diffusion equations. Phys. Rev. E 65, 1103–1106 (2002) 35. Meerschaert, M.M., Benson, D.A., Scheffler, H.P., Becker-Kern, P.: Governing equations and solutions of anomalous random walk limits. Phys. Rev. E 66, 102R–105R (2002) 36. Meerschaert, M.M., Scheffler, H.P.: Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. Wiley Interscience, New York (2001) 37. Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley and Sons, New York (1993) 38. Miyadera, I., Ôharu, S.: Approximation of semi-groups of nonlinear operators. Tôhoku Math. J. (2) 22, 24–47 (1970) 39. Morales, J., Carlo, T.: The effects of plant distribution and frugivore density on the scale and shape of dispersal kernels. Ecology, to appear (2005)
Fractional reaction-diffusion equation 21 40. Murray, J.D.: Mathematical biology. I,II, Interdisciplinary Applied Mathematics, vol. 17,18, third edn. Springer-Verlag, New York (2002) 41. Neubert, M., Caswell, H.: Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations. Ecology 81(6), 1613–1628 (2000) 42. Nolan, J.P.: Numerical calculation of stable densities and distribution functions. Heavy tails and highly volatile phenomena. Comm. Statist. Stochastic Models 13(4), 759–774 (1997). 43. Paradis, E., Baillie, S.R., Sutherland, W.J.: Modeling large-scale dispersal distances. Ecological Modelling 151(2-3), 279–292 (2002) 44. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential equations, Applied Mathematical Sciences, vol. 44. Springer-Verlag, New York (1983) 45. Raberto, M., Scalas, E., Mainardi, F.: Waiting-times and returns in highfrequency financial data: an empirical study. Physica A 314, 749–755 (2002) 46. Sabatelli, L., Keating, S., Dudley, J., Richmond, P.: Waiting time distributions in financial markets. Eur. Phys. J. B 27, 273–275 (2002) 47. Saichev, A.I., Zaslavsky, G.M.: Fractional kinetic equations: solutions and applications. Chaos 7(4), 753–764 (1997) 48. Samko, S., Kilbas, A., Marichev, O.: Fractional Integrals and derivatives: Theory and Applications. Gordon and Breach, London (1993) 49. Samorodnitsky, G., Taqqu, M.S.: Stable Non-Gaussian Random Processes. Chapman & Hall/CRC (1994) 50. Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge studies in advanced mathematics. Cambridge University Press (1999) 51. Scalas, E., Gorenflo, R., Mainardi, F.: Fractional calculus and continuous-time finance. Phys. A 284, 376–384 (2000) 52. Scalas, E.: The application of continuous-time random walks in finance and economics. Physica A 362 225–239 (2006) 53. Scalas, E., Gorenflo, R., Luckock, H., Mainardi, F., Mantelli, M., Raberto, M.: On the Intertrade Waiting-time Distribution. Finance Letters 3, 38–43 (2005) 54. Schilling, R.L.: Growth and Hölder conditions for sample paths of Feller proceses. Probability Theory and Related Fields 112, 565–611 (1998) 55. Schumer, R., Benson, D.A., Meerschaert, M.M., Baeumer, B.: Multiscaling fractional advection-dispersion equations and their solutions. Water Resources Research 39, 1022–1032 (2003) 56. Schumer, R., Benson, D.A., Meerschaert, M.M., Wheatcraft, S.W.: Eulerian derivation of the fractional advection-dispersion equation. Journal of Contaminant Hydrology 48, 69–88 (2001) 57. Sokolov, I.M., Klafter, J.: From diffusion to anomalous diffusion: a century after Einstein’s Brownian motion. Chaos 15(2), 026,103, 7 (2005) 58. Soons, M.B., Heil, G.W., Nathan, R., Katul, G.G.: Determinants of longdistance seed dispersal by wind in grasslands. Ecology 85(11), 3056–3068 (2004) 59. Tackenberg, O.: Modeling long-distance dispersal of plant diaspores by wind. Ecological Monographs 73(2), 173–189 (2003) 60. Tackenberg, O., Poschlod, P., Kahmen, S.: Dandelion seed dispersal: The horizontal wind speed does not matter for long-distance dispersal - it is updraft! Plant Biology 5(5), 451–454 (2003) 61. Zaslavsky, G.: Fractional kinetic equation for hamiltonian chaos. chaotic advection, tracer dynamics and turbulent dispersion. Phys. D 76, 110–122 (1994)
Page 1 and 2: Noname manuscript No. (will be inse
Page 3 and 4: Fractional reaction-diffusion equat
Page 19: Fractional reaction-diffusion equat

Fractional reaction-diffusion equation for species ... - ResearchGate

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?