Have a personal or library account? Click to login

On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives

Open Access
|Sep 2017

References

  1. [1] Anber A., Belarbi S., Dahmani Z. (2013), New existence and uniqueness results for fractional Di erential equations, An. St. Univ. Ovidius Con- stanta, 21, n.3, 33-41.10.2478/auom-2013-0040
  2. [2] Cernea A. (2015), Some remarks on a fractional integro-di erential inclu- sion with boundary conditions, An. St. Univ. Ovidius Constanta, 23, n.1, 73-82.10.1515/auom-2015-0006
  3. [3] Mainardi F. (1996), The fundamental solutions for the fractional di usion-wave equation, Appl. Math. Lett., 9, n.6, 23-28.10.1016/0893-9659(96)00089-4
  4. [4] Mainardi F. (1996), Fractional relaxation-oscillation and fractional di usion-wave phenomena, Chaos, Solitons and Fractals, 7, n.9, 1461-1477.10.1016/0960-0779(95)00125-5
  5. [5] Angulo J.M., Ruiz-Medina, M.D., Anh V.V., Greckosch W. (2000), Frac- tional di usion and fractional heat equation, Adv. in Appl. Probab., 32, 1077-1099.10.1239/aap/1013540349
  6. [6] Orsingher E., Beghin L. (2009), Fractional di usion equations and pro- cesses with randomly-varying time, Ann. Probab., 37, n.1, 206-249.10.1214/08-AOP401
  7. [7] Orsingher, E., Beghin, L. (2004), Time-fractional equations and telegraph processes with Brownian time, Probability Theory and Related Fields, 128, 141-160.10.1007/s00440-003-0309-8
  8. [8] Laskin, N. (2003), Fractional Poisson process, Communications in Non- linear Science and Numerical Simulation, , 8, 201-213.10.1016/S1007-5704(03)00037-6
  9. [9] Mainardi F., Goreno R., Scalas E. (2004), A fractional generalization of the Poisson processes, Vietnam J. Math., 32, 53-64.
  10. [10] Beghin L., Orsingher E. (2009), Fractional Poisson processes and related planar random motions, Electron. J. Probab., 14, n.61, 1790-1826.10.1214/EJP.v14-675
  11. [11] Meerschaert M. M. Nane, E., Veillaisamy P. (2011), The fractional Pois- son process and the inverse stable subordinator. Electron. J. Probab., 59, 1600-1620.10.1214/EJP.v16-920
  12. [12] Karlin, S., Taylor, H.M. (1981), A Second Course in Stochastic Processes. Academic Press, London.
  13. [13] Beghin. L. (2012),Fractional relaxation equations and Brownian crossing probabilities of a random boundary. Adv. in Appl. Probab., 44, 479-505.10.1017/S0001867800005693
  14. [14] Hilfer, R., Anton, L. (1995), Fractional master equations and fractal ran- dom walks. Phys. Rev. E 51 848{851.10.1103/PhysRevE.51.R848
  15. [15] Kilbas A.A., Srivastava H.M., Trujillo J.J. (2006), Theory and Appli- cations of Fractional Di erential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam.
  16. [16] Podlubny I. (1999), Fractional Di erential Equations, San Diego:Academic Press.
  17. [17] Baleanu D, Diethelm K, Scalas E, Trujillo J. (2012), Fractional calculus models and numerical methods. Singapore: World Scientific.10.1142/8180
  18. [18] G. Samko, A. Kilbas, O. Marichev, (1993), Fractional integrals and derivatives: Theory and applications, Gordon and Breach.
  19. [19] Samorodnitsky G., Taqqu M.S. (1994), Stable Non-Gaussian Random Processes. Chapman Hall, New York.
  20. [20] Hahn M.G., Kobayashi K., Umarov S. (2001), Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion, Proc. Amer. Math. Soc., 139, n.2, 691-705.10.1090/S0002-9939-2010-10527-0
  21. [21] Uchaikin V.V., Zolotarev V.M. (1999), Chance and Stability: Stable Dis- tributions and their Applications, VSP, Utrecht.10.1515/9783110935974
  22. [22] D'Ovidio M. (2011), On the fractional counterpart of the higher-order equations, Statist. Probab. Lett., 81, 1929-1939.10.1016/j.spl.2011.08.004
  23. [23] Beghin L., Macci C. (2012), Alternative forms of compound fractional Poisson processes, Abstr. Appl. Anal., 2012, 1-30. 10.1155/2012/747503
DOI: https://doi.org/10.1515/auom-2016-0045 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 5 - 19
Submitted on: Jun 20, 2015
Accepted on: Sep 25, 2015
Published on: Sep 21, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 Mohsen Alipour, Dumitru Baleanu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.