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References
- Applebaum, David. Lévy processes and stochastic calculus. Second edition. Cambridge Studies in Advanced Mathematics, 116. Cambridge University Press, Cambridge, 2009. xxx+460 pp. ISBN: 978-0-521-73865-1 MR2512800
- Baleanu, Dumitru; Golmankhaneh, Ali Khalili; Golmankhaneh, Alireza Khalili; Baleanu, Mihaela Cristina. Fractional electromagnetic equations using fractional forms. Internat. J. Theoret. Phys. 48 (2009), no. 11, 3114--3123. MR2546691
- Ben Adda, Faycal. The differentiability in the fractional calculus. Proceedings of the Third World Congress of Nonlinear Analysts, Part 8 (Catania, 2000). Nonlinear Anal. 47 (2001), no. 8, 5423--5428. MR1974748
- Bertoin, Jean. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564
- Bolster, Diogo; Benson, David A.; Meerschaert, Mark M.; Baeumer, Boris. Mixing-driven equilibrium reactions in multidimensional fractional advection-dispersion systems. Phys. A 392 (2013), no. 10, 2513--2525. MR3038326
- Caputo, M.: Linear models of dissipation whose Q is almost frequency independent, phGeophysical Journal of the Royal Astronomical Society, 13, (1967), 529--539. MR2379269
- Dalla Riva, M.; Yakubovich, S. On a Riemann-Liouville fractional analog of the Laplace operator with positive energy. Integral Transforms Spec. Funct. 23 (2012), no. 4, 277--295. MR2903489
- D'Ovidio, M.: Wright functions governed by fractional directional derivatives and fractional advection diffusion equations, phMethods and Applications of Analysis, (2014). To appear.
- D'Ovidio, Mirko. Continuous random walks and fractional powers of operators. J. Math. Anal. Appl. 411 (2014), no. 1, 362--371. MR3118491
- Ervin, Vincent J.; Roop, John Paul. Variational solution of fractional advection dispersion equations on bounded domains in $\Bbb R^ d$. Numer. Methods Partial Differential Equations 23 (2007), no. 2, 256--281. MR2289452
- GadElkarim, J.J., Magin, R.M., Meerschaert, M.M., Capuani, S., Palombo, M., Kumar, A., Leow, A.D.: Fractional order generalization of anomalous diffusion as a multidimensional extension of the transmission line equation, phIEEE Journal on Emerging and Selected Topics in Circuits and Systems, 3(3), (2013), 432--441.
- Hille, Einar; Phillips, Ralph S. Functional analysis and semi-groups. Third printing of the revised edition of 1957. American Mathematical Society Colloquium Publications, Vol. XXXI. American Mathematical Society, Providence, R. I., 1974. xii+808 pp. MR0423094
- Jacob, N. Pseudo differential operators and Markov processes. Vol. III. Markov processes and applications. Imperial College Press, London, 2005. xxviii+474 pp. ISBN: 1-86094-568-6 MR2158336
- Kampé de Fériet, J. Random solutions of partial differential equations. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. III, pp. 199--208. University of California Press, Berkeley and Los Angeles, 1956. MR0084927
- Komatsu, Hikosaburo. Fractional powers of operators. Pacific J. Math. 19 1966 285--346. MR0201985
- Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni. The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 (2001), no. 2, 153--192. MR1829592
- Metzler, Ralf; Klafter, Joseph. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37 (2004), no. 31, R161--R208. MR2090004
- Meerschaert, M.M., Benson, D.A. and Baeumer, B.: Multidimensional advection and fractional dispersion, phPhysical Review E, 59, (1999), 5026--5028.
- Meerschaert, Mark M.; Mortensen, Jeff; Scheffler, Hans-Peter. Vector Grunwald formula for fractional derivatives. Fract. Calc. Appl. Anal. 7 (2004), no. 1, 61--81. MR2077400
- Meerschaert, M.M., Mortensen, J. and Wheatcraft, S.W.: Fractional vector calculus for fractional advection-dispersion, phPhysica A, 367, (2006), 181--190.
- Miškinis, Paulius. On integral representation of the translation operator. Math. Model. Anal. 17 (2012), no. 1, 100--112. MR2904379
- Orsingher, Enzo; Beghin, Luisa. Fractional diffusion equations and processes with randomly varying time. Ann. Probab. 37 (2009), no. 1, 206--249. MR2489164
- Ostoja-Starzewski, Martin. Electromagnetism on anisotropic fractal media. Z. Angew. Math. Phys. 64 (2013), no. 2, 381--390. MR3041577
- Paradisi, P., Cesari, R., Mainardi, F. and Tampieri, F.: The fractional Fick's law for non-local transport processes, phPhysica A, 293 (1-2), (2001), 130 --142
- Samko, Stefan G.; Kilbas, Anatoly A.; Marichev, Oleg I. Fractional integrals and derivatives. Theory and applications. Edited and with a foreword by S. M. Nikolʹskiĭ. Translated from the 1987 Russian original. Revised by the authors. Gordon and Breach Science Publishers, Yverdon, 1993. xxxvi+976 pp. ISBN: 2-88124-864-0 MR1347689
- Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932
- Schumer, R., Meerschaert, M.M. and Baeumer, B.: Fractional advection-dispersion equations for modeling transport at the Earth surface, phJournal of Geophysical Research: Earth Surface, 114(F4), (2009)
- Tarasov, Vasily E. Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media. Nonlinear Physical Science. Springer, Heidelberg; Higher Education Press, Beijing, 2010. xvi+504 pp. ISBN: 978-3-642-14002-0; 978-7-04-029473-6 MR2796453
- Tarasov, Vasily E. Fractional vector calculus and fractional Maxwell's equations. Ann. Physics 323 (2008), no. 11, 2756--2778. MR2463217
- Tarasov, Vasily E. Fractional generalization of gradient systems. Lett. Math. Phys. 73 (2005), no. 1, 49--58. MR2168006
- Traple, Janusz. Markov semigroups generated by Poisson driven differential equations. Bull. Polish Acad. Sci. Math. 44 (1996), no. 2, 161--182. MR1416422
- Wheatcraft, S.W. and Meerschaert, M.M.: Fractional conservation of mass, phAdvances in Water Resources, 31, (2008), 1377--1381.
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