Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates

• Autorzy: Povstenko Y.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fractional equations; Cauchy problem; Laplace transforms; Hankel and Laplace transforms

PL

równanie ułamkowe; problem Cauchy'ego; transformaty Laplace'a; transformata Hankela

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2009
• Tom: Vol. 14
• Strony: 97--104
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Povstenko Y.

• 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.