Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-Fractional Derivatives

We consider an initial/boundary value problem for linear diffusion equation with multiple fractional time derivatives and prove the regularity of the solution. The regularity argument implies the unique existence of the solution.

[1]  Masahiro Yamamoto,et al.  Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems , 2011 .

[2]  Yury Luchko,et al.  Maximum principle for the generalized time-fractional diffusion equation , 2009 .

[3]  Francesco Mainardi,et al.  The time fractional diffusion-wave equation , 1995 .

[4]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[5]  Anatoly N. Kochubei,et al.  Cauchy problem for fractional diffusion equations , 2003 .

[6]  Roberto Monaco,et al.  Waves and Stability in Continuous Media , 1991 .

[7]  K. Burrage,et al.  Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain , 2012 .

[8]  F. Mainardi The fundamental solutions for the fractional diffusion-wave equation , 1996 .

[9]  Yury F. Luchko Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation , 2011 .

[10]  I. Podlubny Fractional differential equations , 1998 .

[11]  Yury F. Luchko Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation , 2010, Comput. Math. Appl..

[12]  J. Prüss Evolutionary Integral Equations And Applications , 1993 .

[13]  Emilia Bazhlekova,et al.  The abstract Cauchy problem for the fractional evolution equation , 1998 .

[14]  O. Agrawal Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain , 2002 .

[15]  Daniel B. Henry Geometric Theory of Semilinear Parabolic Equations , 1989 .

[16]  Yasuhiro Fujita,et al.  INTEGRODIFFERENTIAL EQUATION WHICH INTERPOLATES THE HEAT EQUATION AND THE WAVE EQUATION I(Martingales and Related Topics) , 1989 .

[17]  W. Schneider,et al.  Fractional diffusion and wave equations , 1989 .

[18]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[19]  R. Nigmatullin The Realization of the Generalized Transfer Equation in a Medium with Fractal Geometry , 1986, January 1.