The distinguishing features of the fundamental solution to the diffusion-wave equation

• Autorzy: Povstenko J.
• Języki publikacji: EN

Abstrakty

EN

The time-fractional diffusion-wave equation with the Caputo derivative is considered. The typical features of the solution to the Cauchy problem for this equation are discussed depending on values of the order of fractional derivative.

Słowa kluczowe

EN

Caputo derivative; diffusion-wave equation

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2008
• Tom: Vol. 7, nr 2
• Strony: 63--70
• Opis fizyczny: Bibliogr. 14 poz., fig.

Twórcy

autor

Povstenko J.

• Institute of Mathematics and Computer Science, Jan Długosz University of Częstochowa,

Bibliografia

• [1] Metzler R., Klafter J., The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep., 339, 2000, 1-77.
• [2] Metzler R., Klafter J., The restaurant at the end of the random walk: recent developments in the decsription of anomalous transport by fractional dynamics, J. Phys. A: Math. Gen. 2004, 37, R161-R208.
• [3] Zaslavsky G.M., Chaos, fractional kinetics, and anomalous transport, Phys. Rep. 2002, 371, 461-580.
• [4] Gorenflo R., Mainardi F., Random walk models for space-fractional diffusion processes, Fractional Calculus Applied Analysis 1998, 1, 167-191.
• [5] Samko S.G., Kilbas A.A., Marichev O.O., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Amsterdam 1993.
• [6] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.
• [7] Gorenflo R., Mainardi F., Fractional calculus: integral and differential equations of fractional order, In: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York 1997, 223-276.
• [8] Mainardi F., The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett. 1996, 9, 23-28.
• [9] Wyss W., The fractional diffusion equation, J. Math. Phys. 1986, 27, 2782-2785.
• [10] Schneider W.R., Wyss W., Fractional diffusion and wave equations, J. Math. Phys. 1989, 30, 134-144.
• [11] Fujita Y., Integrodifferential equation which interpolates the heat equation and the wave equation, Osaka J. Math. 1990, 27, 309-321.
• [12] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F., Higher Transcendental Functions, vol. 3, McGraw-Hill, New York 1955.
• [13] Nigmatullin R.R., On the theoretical explanation of the “universal response”, Phys. Stat. Sol. (b) 1984, 123, 739-745.
• [14] Green A.E., Naghdi P.M., Thermoelasticity without energy dissipation, J. Elast. 1993, 31, 189-208.