[1]
Adams, E. E. and Gelhar, L. W., Field study of dispersion in a heterogeneous aquifer 2: Spatial moments analysis, Water Resources Research, 28 (1992), pp. 3293–3307.

[2]
Bazhlekova, E., Properties of the fundamental and the impulse-response solutions of multi-term fractional differential equations, in: Kiryakova, V. (Eds.), Complex Analysis and Applications’ 13, Bulg. Acad. Sci. Sofia, (2013), pp. 55–64.

[3]
Benson, D. A., The Fractional Advection-Dispersion Equation: Development and Application, University of Nevada, Reno, 1998.

[4]
Berkowitz, B., Scher, H. and Silliman, S. E., Anomalous transport in laboratory-scale heterogeneous porous media, Water Resources Research, 36 (2000), pp. 149–158.

[5]
Caponetto, R., Dongola, G., Fortuna, L. and Petras, I., Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore, 2010.

[6]
Cheng, J., Nakagawa, J., Yamamoto, M. and Yamazaki, T., Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation, Inverse Problems, 25 (2009), 115002.

[7]
Courant, R. and Hilbert, D., Methods of Mathematical Physics, Interscience Publishers, New York, 1989.

[8]
Daftardar-Gejji, V. and Bhalekar, S., Boundary value problems for multi-term fractional differential equations, J. Math. Anal. Appl., 345 (2008), pp. 754–765.

[9]
Hatano, Y. and Hatano, N., Dispersive transport of ions in column experiments: an explanation of long-tailed profiles, Water Resources Research, 34 (1998), pp. 1027–1033.

[10]
Jia, X. Z., Li, G. S., Sun, C. L. and Du, D. H., Simultaneous inversion for a diffusion coefficient and a spatially dependent source term in the SFADE, Inverse Problems Sci. Eng., 24 (2016), pp. 832–859.

[11]
Jiang, H., Liu, F., Turner, I. and Burrage, K., Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain, Comput. Math. Appl., 64 (2012), pp. 3377–3388.

[12]
Jin, B. T., Lazarov, R., Liu, Y. K. and Zhou, Z., The Galerkin finite element method for a multi-term time-fractional diffusion equation, J. Comput. Phys., 281 (2015), pp. 825–843.

[13]
Jin, B. T. and Rundell, W., An inverse problem for a one-dimensional time-fractional diffusion problem, Inverse Problems, 28 (2012), 075010.

[14]
Jin, B. T. and Rundell, W., A tutorial on inverse problems for anomalous diffusion processes, Inverse Problems, 31 (2015), 035003.

[15]
Keisler, H. J., Elementary Calculus, An Infinitesimal Approach, Prindle, Weber & Schmidt, Boston & Massachusetts, 1986.

[16]
Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

[17]
Kirsch, A., An Introduction to Mathematical Theory of Inverse Problems, Springer, New York, 1996.

[18]
Li, G. S., Sun, C. L., Jia, X. Z. and Du, D. H., Numerical solution to the multi-term time fractional diffusion equation in a finite domain, Numer. Math. Theory Method Appl., 9 (2016), pp. 337–357.

[19]
Li, G. S., Zhang, D. L., Jia, X. Z. and Yamamoto, M., Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation, Inverse Problems, 29 (2013), 065014.

[20]
Li, K. T. and Ma, Y. C., Hilbert Space Methods for Mathematics-Physics Equations: Part 2 (in Chinese), Xi’an, Xi’an Jiaotong University Press, 1992.

[21]
Li, Z. Y., Imanuvilov, O. Y. and Yamamoto, M., Uniqueness in inverse boundary value problems for fractional diffusion equations, Inverse Problems, 32 (2016), 015004.

[22]
Li, Z. Y., Liu, Y. K. and Yamamoto, M., Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients, Appl. Math. Comput., 257 (2015), pp. 381–397.

[23]
Li, Z. Y. and Yamamoto, M., Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation, Appl. Anal., 94 (2015), pp. 570–579.

[24]
Liu, F., Meerschaert, M. M. and McGough, R. J. et al., Numerical methods for solving the multi-term time-fractional wave-diffusion equations, Fractional Calculus Appl. Anal., 16 (2013), pp. 9–25.

[25]
Liu, J. J. and Yamamoto, M., A backward problem for the time-fractional diffusion equation, Appl. Anal., 89 (2010), pp. 1769–1788.

[26]
Liu, J. J., Yamamoto, M. and Yan, L., On the reconstruction of unknown time dependent boundary sources for time fractional diffusion process by distributing measurement, Inverse Problems, 32 (2016), 015009.

[27]
Luchko, Y., Maximum principle for the generalized time-fractional diffusion equation, J. Math. Anal. Appl., 351 (2009), pp. 218–223.

[28]
Luchko, Y., Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation, Comput. Math. Appl., 59 (2010), pp. 1766–1772.

[29]
Luchko, Y., Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation, J. Math. Anal. Appl., 374 (2011), pp. 538–548.

[30]
Luchko, Y., Rundell, W., Yamamoto, M. and Zuo, L. H., Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation, Inverse Problems, 29 (2013), 065019.

[31]
Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press, London, 2010.

[32]
Miller, L. and Yamamoto, M., Coefficient inverse problem for a fractional diffusion equation, Inverse Problems, 29 (2013), 075013.

[33]
Murio, D. A., Stable numerical solution of fractional-diffusion inverse heat conduction problem, Comput. Math. Appl., 53 (2007), pp. 1492–501.

[34]
Podlubny, I., Fractional Differential Equations, Academic, San Diego, 1999.

[35]
Sakamoto, K. and Yamamoto, M., Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl., 382 (2011), pp. 426–447.

[36]
Tuan, V. K., Inverse problem for fractional diffusion equation, Fract. Calc. Appl. Anal., 14 (2011), pp. 31–55.

[37]
Wei, T., Li, X. L. and Li, Y. S., An inverse time-dependent source problem for a time-fractional diffusion equation, Inverse Problems, 32 (2016), 085003.

[38]
Wei, T. and Wang, J. G., A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation, Appl. Numer. Math., 78 (2014), pp. 95–111.

[39]
Wei, T. and Wang, J. G., A modified quasi-boundary value method for the backward time-fractional diffusion problem, ESAIM:M2AN, 48 (2014), pp. 603–621.

[40]
Yamamoto, M. and Zhang, Y., Conditional stability in determining a zeroth-order coefficient in a half-order fractional diffusion equation by a Carleman estimate, Inverse problems, 28 (2012), 105010.

[41]
Zhang, D. L., Li, G. S., Jia, X. Z. and Li, H. L., Simultaneous inversion for space-dependent diffusion coefficient and source magnitude in the time fractional diffusion equation, J. Math. Research, 5 (2013), pp. 65–78.

[42]
Zhang, Z. D., An undetermined coefficient problem for a fractional diffusion equation, Inverse Problems, 32 (2016), 015011.

[43]
Zhang, Z. Q. and Wei, T., Identifying an unknown source in time-fractional diffusion equation by a truncation method, Appl. Math. Comput., 219 (2013), pp. 5972–5983.