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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 10
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Articles

Cauchy problem for fractional diffusion-wave equations with variable coefficients

Pages 2211-2242 | Received 17 Oct 2013, Accepted 08 Dec 2013, Published online: 24 Jan 2014

References

  • Mainardi F. Fractional calculus and waves in linear viscoelasticity. London: Imperial College Press; 2010.
  • Kochubei AN. Fractional-order diffusion. Diff. Equat. 1990;26:485–492.
  • Eidelman SD, Kochubei AN. Cauchy problem for fractional diffusion equations. J. Diff. Equat. 2004;199:211–255.
  • Kochubei AN. Fractional-hyperbolic systems. Fract. Calc. Appl. Anal. 2013;16:860–873.
  • Clément Ph, Gripenberg G, Londen S-O. Regularity properties of solutions of fractional evolution equations. Lect. Notes Pure Appl. Math. 2001;215:235–246.
  • Clément Ph, Londen S-O, Simonett G. Quasilinear evolutionary equations and continuous interpolation spaces. J. Diff. Equat. 2004;196:418–447.
  • Fujita Y. Integrodifferential equation which interpolates the heat equation and the wave equation. Osaka J. Math. 1990;27:309–321.
  • Hanyga A. Multidimensional solutions of time-fractional diffusion-wave equations. Proc. Roy. Soc. London, Ser. A. 2002;458:933–957.
  • Kexue Li, Jigen P. Fractional abstract Cauchy problem. Integral Equ. Oper. Theory. 2011;70:333–361.
  • Luchko Yu, Mainardi F, Povstenko Yu. Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Comp. Math. Appl. 2013;66:774–784.
  • Mainardi F. The fundamental solution for the fractional diffusion-wave equation. Appl. Math. Lett. 1996;9:23–28.
  • Mainardi F, Pagnini G. The Wright functions as solutions of the time-fractional diffusion equation. Appl. Math. Comput. 2003;141:51–62.
  • Petzeltová H, Prüss J. Global stability of a fractional partial differential equation. J. Integral Equat. Appl. 2000;12:323–347.
  • Pskhu AV. The fundamental solution of a diffusion-wave equation of fractional order. Izvestiya: Math. 2009;73:351–392.
  • Schneider WR, Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 1989;30:134–144.
  • Vergara V, Zacher R. Lyapunov functions and convergence to steady state for differential equations of fractional order. Math. Z. 2008;259:287–309.
  • Prüss J. Evolutionary integral equations and applications. Basel: Birkhäuser; 1993.
  • Eidelman SD. Parabolic systems. Amsterdam: North-Holland; 1969.
  • Eidelman SD, Ivasyshen SD, Kochubei AN. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Basel: Birkhäuser; 2004.
  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ):Prentice-Hall; 1964.
  • Kochubei AN. Fractional-parabolic systems. Potential Anal. 2012;37:1–30.
  • Samko SG, Kilbas AA, Marichev OI. Fractional integrals and derivatives: theory and applications. New York (NY): Gordon and Breach; 1993.
  • Podlubny I, Chen Y. Adjoint fractional differential expressions and operators. Proc. ASME 2007 Conf. IDET/CIE 2007. Paper DETC 2007–35005; Las Vegas, Nevada, USA. 6 p.
  • Miranda C. Partial differential equations of elliptic type. Berlin: Springer; 1970.
  • Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.

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