zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fractional-order diffusion-wave equation. (English) Zbl 0846.35001
Summary: The fractional-order diffusion-wave equation is an evolution equation of order $\alpha\in (0, 2]$ which continues to the diffusion equation when $\alpha\to 1$ and to the wave equation when $\alpha\to 2$. 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.

35A05General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI
[1] El-Sayed, A. M. A. (1992). On the fractional differential equations,Applied Mathematics and Computation.49(2--3), 205--213. · Zbl 0757.34005 · doi:10.1016/0096-3003(92)90024-U
[2] El-Sayed, A. M. A. (1993). Linear differential equations of fractional orders,Applied Mathematics and Computation,55, 1--12. · Zbl 0772.34013 · doi:10.1016/0096-3003(93)90002-V
[3] El-Sayed, A. M. A. (1995). Fractional order evolution equations,Journal of Fractional Calculus,7(May), to appear. · Zbl 0839.34069
[4] El-Sayed, A. M. A., and Ibrahime, A. G. (n.d.). Multivalued fractional differential equation,Applied Mathematics and Computation, to appear.
[5] Gelfand, I. M., and Shilove, G. E. (1958).Generalized Functions, Vol. 1. Moscow.
[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.
[7] Schnrider, W. R., and Wyss, W. (1989). Fractional diffusion and wave equations,Journal of Mathematical Physics,30. · Zbl 0692.45004
[8] Wyss, W. (1986). Fractional diffusion equation,Journal of Mathematical Physics,27. · Zbl 0632.35031