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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
El-Sayed, A. M. A. (1992). On the fractional differential equations,Applied Mathematics and Computation.49(2–3), 205–213.
El-Sayed, A. M. A. (1993). Linear differential equations of fractional orders,Applied Mathematics and Computation,55, 1–12.
El-Sayed, A. M. A. (1995). Fractional order evolution equations,Journal of Fractional Calculus,7(May), to appear.
El-Sayed, A. M. A., and Ibrahime, A. G. (n.d.). Multivalued fractional differential equation,Applied Mathematics and Computation, to appear.
Gelfand, I. M., and Shilove, G. E. (1958).Generalized Functions, Vol. 1. Moscow.
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.
Schnrider, W. R., and Wyss, W. (1989). Fractional diffusion and wave equations,Journal of Mathematical Physics,30.
Wyss, W. (1986). Fractional diffusion equation,Journal of Mathematical Physics,27.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
El-Sayed, A.M.A. Fractional-order diffusion-wave equation. Int J Theor Phys 35, 311–322 (1996). https://doi.org/10.1007/BF02083817
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02083817