[1]

E.E. Adams, L.W. Gelhar, Field study of dispersion in a heterogeneous aquifer 2. Spatial moments analysis. *Water Resources Res*. 28, No 12 (1992), 3293–3307.Google Scholar

[2]

R.A. Adams, *Sobolev Spaces*. Academic Press, New York (1975).Google Scholar

[3]

M. Al-Refai, Y. Luchko, Maximum principles for the fractional diffusion equations with the Riemann-Liouville fractional derivative and their applications. *Fract. Calc. Appl. Anal*. 17, No 2 (2014), 483–498; ; http://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.CrossrefGoogle Scholar

[4]

J.R. Cannon, S.P. Esteva, An inverse problem for the heat equation. *Inverse Problems* 2, No 4 (1986), 395–403.Google Scholar

[5]

R. Courant, D. Hilbert, *Methods of Mathematical Physics*. Interscience, New York (1953).Google Scholar

[6]

L.C. Evans, *Partial Differential Equations*, 2nd ed. American Mathematical Society, Providence - RI (2010).Google Scholar

[7]

D. Gilbarg, N.S. Trudinger, *Elliptic Partial Differential Equations of Second Order*. Springer, Berlin (2001).Google Scholar

[8]

M. Ginoa, S. Cerbelli, H.E. Roman, Fractional diffusion equation and relaxation in complex viscoelastic materials. *Phys. A* 191, No 1 (1992), 449–453.Google Scholar

[9]

R. Gorenflo, A.A. Kilbas, F. Mainardi, S.V. Rogosin, *Mittag-Leffler Functions, Related Topics and Applications*. Springer, Berlin (2014).Google Scholar

[10]

R. Gorenflo, Y. Luchko, M. Yamamoto, Time-fractional diffusion equation in the fractional Sobolev spaces. *Fract. Calc. Appl. Anal*. 18, No 3 (2015), 799–820; ; http://www.degruyter.com/view/j/fca.2015.18.issue-3/issue-files/fca.2015.18.issue-3.xml.CrossrefGoogle Scholar

[11]

Y. Hatano, N. Hatano, Dispersive transport of ions in column experiments: an explanation of long-tailed profiles. *Water Resources Res*. 34, No 5 (1998), 1027–1033.Google Scholar

[12]

B. Jin, R. Lazarov, J. Pasciak, Z. Zhou, Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. *IMA J. Numer. Anal*. 35, No 2 (2015), 561–582.Google Scholar

[13]

B. Jin, R. Lazarov, Z. Zhou, Error estimates for a semidiscrete finite element method for fractional order parabolic equations. *SIAM J. Numer. Anal*. 51, No 1 (2013), 445–466.Google Scholar

[14]

B. Jin, W. Rundell, A tutorial on inverse problems for anomalous diffusion processes. *Inverse Problems* 31, No 3 (2015), 035003.Google Scholar

[15]

F. Liu, P. Zhuang, V. Anh, I. Turner, K. Burrage, Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. *Appl. Math. Comput*. 191, No 1 (2007), 12–20.Google Scholar

[16]

Y. Luchko, Maximum principle for the generalized time-fractional diffusion equation. *J. Math. Anal. Appl*. 351, No 1 (2009), 218–223.Google Scholar

[17]

Y. Luchko, Some uniqueness and existence results for the initial-boundary value problems for the generalized time-fractional diffusion equation. *Comput. Math. Appl*. 59, No 5 (2010), 1766–1772.Google Scholar

[18]

Y. Luchko, R. Gorenflo, An operational method for solving fractional differential equations with the Caputo derivatives. *Acta Math. Vietnam* 24, No 2 (1999), 207–233.Google Scholar

[19]

Y. Luchko, W. Rundell, M. Yamamoto, L. Zuo, Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation. *Inverse Problems* 29, No 6 (2013), 065019.Google Scholar

[20]

M.M. Meerschaert, C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations. *J. Comput. Appl. Math*. 172, No 1 (2004), 65–77.Google Scholar

[21]

R. Metzler, J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach. *Phys. Rep*. 339, No 1 (2000), 1–77.Google Scholar

[22]

R.R. Nigmatullin, The realization of the generalized transfer equation in a medium with fractal geometry. *Phys. Stat. Sol. B* 133, No 1 (1986), 425–430.Google Scholar

[23]

I. Podlubny, *Fractional Differential Equations*. Academic Press, San Diego (1999).Google Scholar

[24]

W. Rundell, X. Xu, L. Zuo, The determination of an unknown boundary condition in a fractional diffusion equation. *Appl. Anal*. 92, No 7 (2013), 1511–1526.Google Scholar

[25]

S. Saitoh, V.K. Tuan, M. Yamamoto, Reverse convolution inequalities and applications to inverse heat source problems. *J. Inequal. Pure Appl. Math*. 3, No 5 (2002), 1–11.Google Scholar

[26]

S. Saitoh, V.K. Tuan, M. Yamamoto, Convolution inequalities and applications. *J. Inequal. Pure Appl. Math*. 4, No 3 (2003), 1–8.Google Scholar

[27]

K. Sakamoto, M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems. *J. Math. Anal. Appl*. 382, No 1 (2011), 426–447.Google Scholar

[28]

E.C. Titchmarsh, The zeros of certain integral functions. *Proc. London Math. Soc*. 2, No 1 (1926), 283–302.Google Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.