International Journal of Theoretical Physics

, Volume 35, Issue 2, pp 311–322

Fractional-order diffusion-wave equation

  • Ahmed M. A. El-Sayed
Article

Abstract

The fractional-order diffusion-wave equation is an evolution equation of order α ε (0, 2] which continues to the diffusion equation when α → 1 and to the wave equation when α → 2. We prove some properties of its solution and give some examples. We define a new fractional calculus (negative-direction fractional calculus) and study some of its properties. We study the existence, uniqueness, and properties of the solution of the negative-direction fractional diffusion-wave problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. El-Sayed, A. M. A. (1992). On the fractional differential equations,Applied Mathematics and Computation.49(2–3), 205–213.Google Scholar
  2. El-Sayed, A. M. A. (1993). Linear differential equations of fractional orders,Applied Mathematics and Computation,55, 1–12.Google Scholar
  3. El-Sayed, A. M. A. (1995). Fractional order evolution equations,Journal of Fractional Calculus,7(May), to appear.Google Scholar
  4. El-Sayed, A. M. A., and Ibrahime, A. G. (n.d.). Multivalued fractional differential equation,Applied Mathematics and Computation, to appear.Google Scholar
  5. Gelfand, I. M., and Shilove, G. E. (1958).Generalized Functions, Vol. 1. Moscow.Google Scholar
  6. Mainardi, F. (1994). On the initial value problem for the fractional diffusion-wave equation, inProceedings VII WASCOM, Bologna 4–7 October 1993, S. Rionero and T. A. Ruggeri, eds., World Scientific, Singapore, in press.Google Scholar
  7. Schnrider, W. R., and Wyss, W. (1989). Fractional diffusion and wave equations,Journal of Mathematical Physics,30.Google Scholar
  8. Wyss, W. (1986). Fractional diffusion equation,Journal of Mathematical Physics,27.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Ahmed M. A. El-Sayed
    • 1
  1. 1.Faculty of ScienceAlexandria UniversityAlexandriaEgypt

Personalised recommendations