References
- Metzler R, Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys Rep. 2000;339(1):1–77.
- Nigmatullin RR. The realization of the generalized transfer equation in a medium with fractal geometry. Phys Status Solidi B Basic Res. 1986;133(1):425–430.
- Zhu TY, Harris JM. Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians. Geophysics. 2014;79(3):T105–T116.
- Ginoa M, Cerbelli S, Roman HE. Fractional diffusion equation and relaxation in complex viscoelastic materials. Phys A. 1992;191(1–4):449–453.
- Adams EE, Gelhar LW. Field study of dispersion in a heterogeneous aquifer 2: spatial moments analysis. Water Resour Res. 1992;28:3293–3307.
- Brockmann D, Hufnagel L, Geisel T. The scaling laws of human travel. Nature. 2006;439(7075):462–465.
- Eidelman SD, Kochubei AN. Cauchy problem for fractional diffusion equations. J Differ Equ. 2004;199(2):211–255.
- Luchko Y. Maximum principle for the generalized time fractional diffusion equation. J Math Anal Appl. 2009;351(1):218–223.
- Luchko Y. Some uniqueness and existence results for the initial-boundary-value problems for the generalized time fractional diffusion equation. Comput Math Appl. 2010;59(5):1766–1772.
- Sakamoto K, Yamamoto M. Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems. J Math Anal Appl. 2011;382(1):426447.
- Zacher R. Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients. J Math Anal Appl. 2008;348(1):137–149.
- Zacher R. Weak solutions of abstract evolutionary integro-differential equations in Hilbert spaces. Funkc Ekvacioj. 2009;52(1):1–18.
- Baeumer B, Kovacs M, Meerschaert MM. Fractional reproduction-dispersal equations and heavy tail dispersal kernels. Bull Math Biol. 2007;69(7):2281–2297.
- Fernandez-Real X, Ros-Oton X. Boundary regularity for the fractional heat equation. Rev R Acad Cien Exactas Fís Nat A. Mat. 2016;110(1):49–64.
- Miller L, Yamamoto M. Coefficient inverse problem for a fractional diffusion equation. Inverse Probl. 2013;29(7):075013.
- Luchko Y, Rundell W, Yamamoto M, et al. Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation. Inverse Probl. 2013;29(6):065019.
- Sakamoto K. Inverse source problem with a final overdetermination for a fractional diffusion equation. Math Control Relat Fields. 2011;1(4):509–518.
- Wei T, Li XL, Li YS. An inverse time-dependent source problem for a time fractional diffusion equation. Inverse Probl. 2016;32(8):085003.
- Liu YK, Rundell W, Yamamoto M. Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. Fractional Calc Appl Anal. 2016;19(4):888–906.
- Cheng J, Nakagawa J, Yamamoto M, et al. Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation. Inverse Probl. 2009;25(11):115002.
- Zhang Y, Xu X. Inverse source problem for a fractional diffusion equation. Inverse Probl. 2011;27(3):257–271.
- Jin B, Rundell W. A tutorial on inverse problems for anomalous diffusion processes. Inverse Probl. 2015;31(3):035003.
- Grubb G. Regularity of spectral fractional Dirichlet and Neumann problems. Math Nachr. 2016;289(7):831–844.
- Tatar S, TInaztepe R, Ulusoy S. Simultaneous inversion for the exponents of the fractional time and space derivatives in the space-time fractional diffusion equation. Appl Anal. 2016;95(1):1–23.
- Jia JX, Peng JG, Gao JH. Bayesian approach to inverse problems for functions with a variable-index Besov prior. Inverse Probl. 2016;32(8):085006.
- Li YS, Wei T. An inverse time-dependent source problem for a time-space fractional diffusion equation. Appl Math Comput. 2018;336(1):257–271.
- Tatar S, Ulusoy S. An inverse source problem for a one-dimensional space–time fractional diffusion equation. Appl Anal. 2015;94(11):2233–2244.
- Jia JX, Peng JG, Yang JQ. Harnack's inequality for a space-time fractional diffusion equation and applications to an inverse source problem. J Differ Equ. 2017;262(8):4415–4450.
- Fisher RA. The wave of advance of advantageous genes. Ann Eugen. 1937;7:355–369.
- Podlubny I. Fractional differential equations. San Diego (CA): Academic Press; 1999.
- Jia JX, Li KX. Maximum principles for a time–space fractional diffusion equation. Appl Math Lett. 2016;62:23–28.
- Pazy A. Semigroups of linear operators and applications to partial differential equations. New York (NY): Springer; 1983.
- Du Q, Gunzburger M, Lehoucq RB, et al. A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Math Model Meth Appl Sci. 2013;23(03):493–540.