References
- Caputo M. Linear models of diffusion whose Q is almost frequency independent, part II. Geophys. J. R. Astron. Soc. 1967;13:529–539.
- Chen QZ, Meerschaert MM, Nane E. Space-time fractional diffusion on bounded domains. J. Math. Anal. Appl. 2012;393:479–488.
- Eidelman SD, Ivasyshen SD, Kochubei AN. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Basel: Birkhäuser; 2004.
- Podlubny I. Fractional differential equations. San Diego (CA): Academic Press; 1999.
- Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.
- Kato T. Perturbation theory for linear operators. Berlin: Springer-Verlag; 1976.
- Sakamoto K, Yamamato M. Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems. J. Math. Anal. Appl. 2011;382:426–447.
- Sakamoto K, Yamamato M. Inverse heat source problem from time distributing overdetermination. Appl. Anal. 2009;88:735–748.
- Sakamoto K, Yamamato M. Inverse source problem with a final overdetermination for a fractional diffusion equation. Math. Control Relat. Fields. 2011;1:509–518.
- Kolokoltsov VN, Veretennikova MA. Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. Fractional Differ. Calculus. Forthcoming.
- Luchko Y. Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Fractional Calculus Appl. Anal. 2012;15:141–160.
- Bogachev V. Measure theory I. Berlin: Springer-Verlag; 2007.
- Adams RA. Sobolev spaces. Vol. 65, Pure and applied mathematics. New York (NY): Academic Press; 1975.
- Stein EM. Singular integrals and differentiability properties of functions. Vol. 30, Princeton Mathematical Series. Princeton (NJ): Princeton University Press; 1970.
- John F. Partial differential equations. Berlin: Springer-Verlag; 1982.
- Renardy M, Rogers RC. An introduction to partial differential equations. New York (NY): Springer-Verlag; 2004.