Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.
Rocznik
Tom
Strony
97--104
Opis fizyczny
Bibliogr. 14 poz., rys.
Twórcy
autor
- Institute of Mathematics and Computer Science Jan Długosz Univetsity in Częstochowa al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland
Bibliografia
- [1] A. Pękalski, K. Sznajd-Weron (Eds.) Anomalous Diffusion: From Basics to Applications. Springer, Berlin 1999.
- [2] R. Hilfer (Ed.) Applications of Fractional Calculus in Physics. World Scientific, Singapore 2000.
- [3] R. Metzler, J. Klafter. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep., 339, 1-77, 2000.
- [4] G.M. Zaslavsky. Chaos, fractional kinetics, and anomalous transport. Phys. Rep., 371, 461-580, 2002.
- [5] R. Metzler, J. Klafter. The restaurant at the end of the random recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A: Math. Gen., 37, R161-R208, 2004.
- [6] F. Mainardi. The fundamental Solutions for the fractional diffusion wave equation. Appl. Math. Lett., 9, 23-28, 1996.
- [7] W. Wyss. The fractional diffusion equation. J. Math. Phys., 27, 27 2785, 1986.
- [8] W.R. Schneider, W. Wyss. Fractional diffusion and wave equations J. Math. Phys., 30, 134-144, 1989.
- [9] A. Hanyga. Multidimensional solutions of time-fractional diffusion-wave equations. Proc. R. Soc. Lond. A, 458, 933-957, 2002.
- [10] Y.Z. Povstenko. Fractional heat conduction equation and associated thermal stress. J. Thermal Stresses, 28, 83-102, 2005.
- [11] Y.Z. Povstenko. Stresses exerted by a source of diffusion in a case i non-parabolic diffusion equation. Int. J. Eng. Sci., 43, 977-991,
- [12] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam 2006.
- [13] P.K. Kythe. Fundamental Solutions for Differential Operators Applications. Birkhäuser, Boston 1996.
- [14] W.R. Schneider, Fractional diffusion, in R. Lima, L. Streit and R. Viela Mendes (Eds.), Dynamics and Stochastic Processes, Lecture Notes Physics, vol. 355, pp. 276-286, Springer, Berlin 1990.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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