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  1. Beghin, Luisa. Pseudoprocesses governed by higher-order fractional differential equations. Electron. J. Probab. 13 (2008), no. 16, 467--485. MR2386739 (2009g:60048)
  2. Beghin, L.; Orsingher, E. Fractional Poisson processes and related planar random motions. Electron. J. Probab. 14 (2009), no. 61, 1790--1827. MR2535014
  3. Beghin, L., Orsingher, E. (2009) Poisson-type processes governed by fractional and higher-order recursive differential equations, arXiv:0910.5855v1, [math.PR], 30 Oct. 2009.
  4. Beghin, L., Orsingher, E. (2010), Moving randomly amid scattered obstacles, Stochastics, vol. 82, n.2, 201-229.
  5. Cahoy, D.O. (2007), Fractional Poisson process in terms of $alpha $-stable densities, Ph.D. Thesis, Case Western University.
  6. Di Crescenzo, Antonio. On random motions with velocities alternating at Erlang-distributed random times. Adv. in Appl. Probab. 33 (2001), no. 3, 690--701. MR1860096 (2002h:60231)
  7. Di Crescenzo, Antonio. Exact transient analysis of a planar random motion with three directions. Stoch. Stoch. Rep. 72 (2002), no. 3-4, 175--189. MR1897914 (2003c:60091)
  8. Gorenflo, R.; Mainardi, F. Fractional calculus: integral and differential equations of fractional order. Fractals and fractional calculus in continuum mechanics (Udine, 1996), 223--276, CISM Courses and Lectures, 378, Springer, Vienna, 1997. MR1611585 (99g:26015)
  9. Gradshteyn, I. S.; Ryzhik, I. M. Table of integrals, series, and products.Translated from the Russian.Sixth edition.Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger.Academic Press, Inc., San Diego, CA, 2000. xlvii+1163 pp. ISBN: 0-12-294757-6 MR1773820 (2001c:00002)
  10. Jumarie, Guy. Fractional master equation: non-standard analysis and Liouville-Riemann derivative. Chaos Solitons Fractals 12 (2001), no. 13, 2577--2587. MR1851079 (2003i:82069)
  11. Lachal, Aimé. Cyclic random motions in $Bbb Rsp d$-space with $n$ directions. ESAIM Probab. Stat. 10 (2006), 277--316 (electronic). MR2247923 (2007k:60036)
  12. Lagerås, Andreas Nordvall. A renewal-process-type expression for the moments of inverse subordinators. J. Appl. Probab. 42 (2005), no. 4, 1134--1144. MR2203828 (2007c:60089)
  13. Laskin, Nick. Fractional Poisson process.Chaotic transport and complexity in classical and quantum dynamics. Commun. Nonlinear Sci. Numer. Simul. 8 (2003), no. 3-4, 201--213. MR2007003 (2004j:60101)
  14. Mainardi F. (1996), The fundamental solutions for the fractional diffusion-wave equation, Applied Mathematics Letters, 9, n.6, 23-28.
  15. Mainardi, Francesco. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals 7 (1996), no. 9, 1461--1477. MR1409912 (97i:26011)
  16. Mainardi F., Raberto, M., Gorenflo R., Scalas E. (2000), Fractional calculus and continuous-time finance II: the waiting-time distribution, Physica A, 287, 468-481.
  17. Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico. A fractional generalization of the Poisson processes. Vietnam J. Math. 32 (2004), Special Issue, 53--64. MR2120631
  18. Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro. Renewal processes of Mittag-Leffler and Wright type. Fract. Calc. Appl. Anal. 8 (2005), no. 1, 7--38. MR2179226
  19. Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro. Beyond the Poisson renewal process: a tutorial survey. J. Comput. Appl. Math. 205 (2007), no. 2, 725--735. MR2329648
  20. Orsingher, Enzo; Beghin, Luisa. Time-fractional telegraph equations and telegraph processes with Brownian time. Probab. Theory Related Fields 128 (2004), no. 1, 141--160. MR2027298 (2005a:60056)
  21. Orsingher, E., Beghin, L. (2009), Fractional diffusion equations and processes with randomly-varying time, Annals of Probability, 37(1), 206-249.
  22. Podlubny, Igor. Fractional differential equations.An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications.Mathematics in Science and Engineering, 198. Academic Press, Inc., San Diego, CA, 1999. xxiv+340 pp. ISBN: 0-12-558840-2 MR1658022 (99m:26009)
  23. Pogorui, A. A.; Rodríguez-Dagnino, Ramón M. One-dimensional semi-Markov evolutions with general Erlang sojourn times. Random Oper. Stochastic Equations 13 (2005), no. 4, 399--405. MR2183564 (2007g:60107)
  24. Prabhakar, Tilak Raj. A singular integral equation with a generalized Mittag Leffler function in the kernel. Yokohama Math. J. 19 (1971), 7--15. MR0293349 (45 #2426)
  25. Repin, O. N.; Saichev, A. I. Fractional Poisson law. Radiophys. and Quantum Electronics 43 (2000), no. 9, 738--741 (2001). MR1910034
  26. Saji Kumar, V. R.; Pillai, R. N. Single server queue with batch arrivals and $alpha$-Poisson distribution. Calcutta Statist. Assoc. Bull. 58 (2006), no. 229-230, 93--103. MR2305408 (2007m:60282)
  27. Saxena, R.K., Mathai, A.M., Haubold, H.J. (2006), Fractional reaction-diffusion equations, Astrophysics and Space Science, 305, 289-296.
  28. Saxena, R.K., Mathai, A.M., Haubold, H.J., (2006), Solutions of fractional reaction-diffusion equations in terms of Mittag-Leffler functions, Intern. Journ. Scient. Research, 15,
  29. Shukla, A. K.; Prajapati, J. C. On a generalization of Mittag-Leffler function and its properties. J. Math. Anal. Appl. 336 (2007), no. 2, 797--811. MR2352981 (2008m:33055)
  30. Uchaikin, Vladimir V.; Sibatov, Renat T. Fractional theory for transport in disordered semiconductors. Commun. Nonlinear Sci. Numer. Simul. 13 (2008), no. 4, 715--727. MR2381497 (2008k:82136)

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