# Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

- Published: 17 Feb 2018

- Shandong University of Technology China (People's Republic of)

- 1
- 2

[9] Cheng J, Nakagawa J, Yamamoto M and Yamazaki T. Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation. Inverse problems, 2009, 25(11): 115002.

[10] Daftardar-Gejji V, Bhalekar S. Boundary value problems for multi-term fractional differential equations. Journal of Mathematical Analysis and Applications, 2008, 345(2): 754-765. [OpenAIRE]

[11] Giona M, Cerbelli S, Roman H E. Fractional diffusion equation and relaxation in complex viscoelastic materials. Physica A: Statistical Mechanics and its Applications, 1992, 191(1- 4): 449-453. [OpenAIRE]

[12] Gorenflo R, Luchko Y, Yamamoto M. Time-fractional diffusion equation in the fractional Sobolev spaces. Fractional Calculus and Applied Analysis, 2015, 18(3): 799-820.

[13] Gorenflo R, Luchko Y, Zabrejko P P. On solvability of linear fractional differential equations in Banach spaces. Fract. Calc. Appl. Anal, 1999, 2(3): 163-177.

[14] Gorenflo R, Mainardi F. Fractional calculus: Integral and differential equations of fractional order, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, New York, (1997) 223-276. [OpenAIRE]

[15] Hatano Y, Hatano N. Dispersive transport of ions in column experiments: An explanation of long-tailed profiles. Water Resources Research, 1998, 34(5): 1027-1033.

[16] Hatano Y, Nakagawa J, Wang S and Yamamoto M. Determination of order in fractional diffusion equation. Journal of Math-for-Industry (JMI), 2013, 5(A): 51-57.

[17] Henry D. Geometric theory of semilinear parabolic equations. Springer, 2006.

[18] Jiang D, Li Z, Liu Y and Yamamoto M. Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations. Inverse Problems, 2017.

[19] Jiang H, Liu F, Turner I and Burrage K. Analytical solutions for the multi-term timespace Caputo-Riesz fractional advection-diffusion equations on a finite domain. Journal of Mathematical Analysis and Applications, 2012, 389(2): 1117-1127.

[20] Jin B, Rundell W. A tutorial on inverse problems for anomalous diffusion processes. Inverse Problems, 2015, 31(3): 035003.

[21] Kian Y, Oksanen L, Soccorsi E and Yamamoto M. Global uniqueness in an inverse problem for time fractional diffusion equations. Journal of Differential Equations, 2018, 264(2): 1146-1170.

[22] Kian Y, Soccorsi E, Yamamoto M. A uniqueness result for time-fractional diffusion equations with space-dependent variable order. arXiv preprint arXiv:1701.04046, 2017.

[23] Kilbas A, Srivastave H, Trujillo J. Theory and Applications of Fractional Differential Equations, North-Hollan Math. Studies, 2006, 204: 135-209.

- 1
- 2