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Fractional-order diffusion-wave equation

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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.

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References

  • El-Sayed, A. M. A. (1992). On the fractional differential equations,Applied Mathematics and Computation.49(2–3), 205–213.

    Google Scholar 

  • El-Sayed, A. M. A. (1993). Linear differential equations of fractional orders,Applied Mathematics and Computation,55, 1–12.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

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El-Sayed, A.M.A. Fractional-order diffusion-wave equation. Int J Theor Phys 35, 311–322 (1996). https://doi.org/10.1007/BF02083817

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  • DOI: https://doi.org/10.1007/BF02083817

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