| [1] |
Adams, EE; Gelhar, LW, Field study of dispersion in a heterogeneous aquifer 2: spatial moments analysis, Water Resour. Res., 28, 3293-3307 (1992) · doi:10.1029/92WR01757 |
| [2] |
Alimov, S.; Ashurov, R., Inverse problem of determining an order of the Caputo time fractional derivative for a subdiffusion equation, J. Inverse Ill Posed Prolems, 28, 651-658 (2020) · Zbl 1461.35207 · doi:10.1515/jiip-2020-0072 |
| [3] |
Alimov, S.; Ashurov, R., Inverse problem of determining an order of the Riemann-Liouville time-fractional derivative, Progr. Fract. Differ. Appl., 8, 4, 1-8 (2022) |
| [4] |
Ashurov, R.; Zunnunov, R., Initial-boundary value and inverse problems for subdiffusion equations in \({\mathbb{R} }^N\), Fract. Differ. Calc., 10, 2, 291-306 (2020) · Zbl 1488.35552 |
| [5] |
Ashurov, R.; Umarov, S., Determination of the order of fractional derivative for subdiffusion equations, Fract. Calc. Appl. Anal., 23, 6, 1647-1662 (2020) · Zbl 1474.35633 · doi:10.1515/fca-2020-0081 |
| [6] |
Ashurov, R.; Umarov, S., An inverse problem of determining orders of systems of fractional pseudo-differential equations, Fract. Calc. Appl. Anal., 25, 1, 109-127 (2022) · Zbl 1503.35247 · doi:10.1007/s13540-021-00006 |
| [7] |
Bateman, H., Higher Transcendental Functions (1953), New York: McGraw-Hill, New York · Zbl 0051.30303 |
| [8] |
Cheng, J.; Nakagawa, J.; Yamamoto, M.; Yamazaki, T., Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation, Inverse Problems, 25 (2009) · Zbl 1181.35322 · doi:10.1088/0266-5611/25/11/115002 |
| [9] |
Courant, R.; Hilbert, D., Methods of Mathematical Physics (1989), Hoboken: Wiley, Hoboken · Zbl 0729.35001 · doi:10.1002/9783527617210 |
| [10] |
Gorenflo, R.; Kilbas, AA; Mainardi, F.; Rogosin, S., Mittag-Leffler Functions, Related Topics and Applications (2020), Cham: Springer, Cham · Zbl 1451.33001 · doi:10.1007/978-3-662-61550-8 |
| [11] |
Hatano, Y.; Hatano, N., Dispersive transport of ions in column experiments: an explanation of long-tailed profiles, Water Resour. Res., 34, 1027-1033 (1998) · doi:10.1029/98WR00214 |
| [12] |
Janno, J., Determination of the order of fractional derivative and a kernel in an inverse problem for a genaralized time fractional diffusion equation, Electron. J. Differ. Equ., 199, 1-28 (2016) · Zbl 1342.35452 |
| [13] |
Janno, J.; Kinash, N., Reconstruction of an order of derivative and a source term in a fractional diffusion equation from final measurements, Inverse Problems, 34 (2018) · Zbl 1474.35694 · doi:10.1088/1361-6420/aaa0f0 |
| [14] |
Jin, BT; Rundell, W., A tutorial on inverse problems for anomalous diffusion processes, Inverse Problems, 31 (2015) · Zbl 1323.34027 · doi:10.1088/0266-5611/31/3/035003 |
| [15] |
Jin, B. T., Kian, Y.: Recovery of the order of derivation for fractional diffusion equations in an unknown medium. ArXiv: 2101.09165 (2021) · Zbl 1492.35426 |
| [16] |
Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M., Global uniqueness in an inverse problem for time fractional diffusion equations, J. Differ. Equ., 264, 1146-1170 (2018) · Zbl 1376.35099 · doi:10.1016/j.jde.2017.09.032 |
| [17] |
Kilbas, AA; Srivastava, HM; Trujillo, JJ, Theory and Applications of Fractional Differential Equations (2006), Amsterdam: Elsevier, Amsterdam · Zbl 1092.45003 |
| [18] |
Kubica, A.; Ryszewska, K.; Yamamoto, M., Theory Time-Fractional Differential Equations an Introduction (2020), Cham: Springer, Cham · Zbl 1485.34002 · doi:10.1007/978-981-15-9066-5 |
| [19] |
Li, GS; Zhang, DL; Jia, XZ; Yamamoto, M., Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation, Inverse Problems, 29 (2013) · Zbl 1281.65125 · doi:10.1088/0266-5611/29/6/065014 |
| [20] |
Li, ZY; Yamamoto, M., Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation, Appl. Anal., 94, 570-579 (2015) · Zbl 1327.35408 · doi:10.1080/00036811.2014.926335 |
| [21] |
Li, Z. Y., Liu, Y. K., Yamamoto, M.: Inverse problems of determining parameters of the fractional partial differential equations. In: Handbook of Fractional Calculus with Applications Vol.2, 431-442, DeGruyter, Berlin (2019) · Zbl 1410.26004 |
| [22] |
Li, ZY; Fujishiro, K.; Li, GS, Uniqueness in the inversion of distributed orders in ultraslow diffusion equations, J. Comput. Appl. Math., 369 (2020) · Zbl 1430.35257 · doi:10.1016/j.cam.2019.112564 |
| [23] |
Luchko, Y., Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation, Comput. Math. Appl., 59, 1766-1772 (2010) · Zbl 1189.35360 |
| [24] |
Podlubny, I., Fractional Differential Equations (1999), Cambridge: Academic Press, Cambridge · Zbl 0924.34008 |
| [25] |
Sakamoto, K.; Yamamoto, M., Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl., 382, 426-447 (2011) · Zbl 1219.35367 · doi:10.1016/j.jmaa.2011.04.058 |
| [26] |
Sun, LL; Li, YS; Zhang, Y., Simultaneous inversion for the potential term and the fractional orders in a multi-term time-fractional diffusion equation, Inverse problems, 37 (2021) · Zbl 1462.35469 · doi:10.1088/1361-6420/abf162 |
| [27] |
Tatar, S.; Ulusoy, S., A uniqueness result for an inverse problem in a space-time fractional diffusion equation, Electron. J. Differ. Equ., 258, 1-9 (2013) · Zbl 1287.65076 |
| [28] |
Yamamoto, M.: Uniqueness in determining the orders of time and spatial fractional derivatives. ArXiv: 2006.15046 (2020) |
| [29] |
Yamamoto, M., Uniqueness in determining fractional orders of derivatives and initial values, Inverse Problems, 37 (2021) · Zbl 1478.35227 · doi:10.1088/1361-6420/abf9e9 |
| [30] |
Zhou, L.; Selim, HM, Application of the fractional advection-dispersion equations in porous media, Soil Sci. Soc. Am. J., 67, 1079-1084 (2003) · doi:10.2136/sssaj2003.1079 |
