[1] |
Jin, L.; Li, L.; Fang, S., The global existence and time-decay for the solutions of the fractional pseudo-parabolic equation, Computers and Mathematics with Applications, 73, 10, 2221-2232 (2017) · Zbl 1386.35443 · doi:10.1016/j.camwa.2017.03.005 |
[2] |
Barenblatt, G. I.; Zheltov, I. P.; Kochina, I., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], Journal of Applied Mathematics and Mechanics, 24, 5, 1286-1303 (1960) · Zbl 0104.21702 · doi:10.1016/0021-8928(60)90107-6 |
[3] |
Benjamin, T. B.; Bona, J. L.; Mahony, J. J., “Model equations for long waves in nonlinear dispersive systems”, Philosophical transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, 272, 1220, 47-78 (1972) · Zbl 0229.35013 |
[4] |
Wang, R.; Li, Y.; Wang, B., Random dynamics of fractional nonclassical diffusion equations driven by colored noise, Discrete & Continuous Dynamical Systems, 39, 7, 4091-4126 (2019) · Zbl 1414.37032 · doi:10.3934/dcds.2019165 |
[5] |
Wang, R.; Shi, L.; Wang, B., Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on \(R^N\), Nonlinearity, 32, 11, 4524-4556 (2019) · Zbl 1423.35419 |
[6] |
Wang, R.; Li, Y.; Wang, B., Bi-spatial pullback attractors of fractional nonclassical diffusion equations on unbounded domains with (p, q)-growth nonlinearities, Applied Mathematics and Optimization, 84, 1, 425-461 (2021) · Zbl 1476.37091 · doi:10.1007/s00245-019-09650-6 |
[7] |
Tuan, N. H.; Caraballo, T., On initial and terminal value problems for fractional nonclassical diffusion equations, Proceedings of the American Mathematical Society, 149, 1, 143-161 (2021) · Zbl 1456.35222 · doi:10.1090/proc/15131 |
[8] |
Tuan, N. H.; Au, V. V.; Xu, R., Semilinear Caputo time-fractional pseudo-parabolic equations, Communications on Pure & Applied Analysis, 20, 2, 583-621 (2021) · Zbl 1460.35381 · doi:10.3934/cpaa.2020282 |
[9] |
Warma, M.; Antil, H.; Verma, D., Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces, Journal of Optimization Theory and Applications, 186, 1, 1-23 (2020) · Zbl 1443.49005 · doi:10.1007/s10957-020-01684-z |
[10] |
Antil, H.; Warma, M., Optimal control of fractional semilinear PDEs, ESAIM, 26, 130 (2020) · Zbl 1439.49008 |
[11] |
Antil, H.; Verma, D.; Warma, M., External optimal control of fractional parabolic PDEs, ESAIM, 26, 20 (2020) · Zbl 1444.35144 · doi:10.1051/cocv/2020005 |
[12] |
Warma, M.; Antil, H.; Khatri, R., External optimal control of nonlocal PDEs, Inverse Problems, 35, 8, 084003 (2019) · Zbl 1461.35221 · doi:10.1088/1361-6420/ab1299 |
[13] |
Warma, M.; Antil, H., Optimal control of the coefficient for fractional and regional fractional \(p\)-Laplace equations: approximation and convergence, Mathematical Control and Related Fields, 9, 1-38 (2019) · Zbl 1423.35388 |
[14] |
Luc, N. H.; Long, L. D.; Hang, L. T. D.; Baleanu, D.; Can, N. H., Identifying the initial condition for space-fractional Sobolev equation, Journal of Applied Analysis & Computation, 11, 5, 2402-2422 (2021) · Zbl 07907283 · doi:10.11948/20200404 |
[15] |
Au, V. V.; Hossein, J.; Hammouch, Z.; Tuan, N. H., On a final value problem for a nonlinear fractional pseudo-parabolic equation, Electronic Research Archive, 29, 1, 1709-1734 (2021) · Zbl 1456.35114 · doi:10.3934/era.2020088 |
[16] |
Nam, D. H. Q.; O’Regan, D.; Long, L. D.; Ngoc, T. B.; Tuan, N. H., Identification of the righthand side in a bi-parabolic equation with final data, Applicable Analysis, 101 (2020) |
[17] |
Ma, Y. K.; Prakash, P.; Deiveegan, A., Generalized Tikhonov methods for an inverse source problem of the time- fractional diffusion equation, Chaos, Solitons and Fractals, 108, 39-48 (2018) · Zbl 1390.35425 · doi:10.1016/j.chaos.2018.01.003 |
[18] |
Engl, H. W.; Hanke, M.; Neubauer, A., Regularization of Inverse Problems (1996), Boston: Kluwer Academic, Boston · Zbl 0859.65054 · doi:10.1007/978-94-009-1740-8 |
[19] |
Han, Y.; Xiong, X.; Xue, X., A fractional Landweber method for solving backward time-fractional diffusion problem, Computers & Mathematcs with Applications, 78, 1, 81-91 (2019) · Zbl 1442.65224 · doi:10.1016/j.camwa.2019.02.017 |
[20] |
Jiang, Z. S.; Wu, J. Y., Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method, Inverse Problems in Science and Engineering, 29, 7, 990-1011 (2021) · Zbl 1473.65167 · doi:10.1080/17415977.2020.1815724 |
[21] |
Yang, F.; Fu, L. J.; Fan, P.; Li, X. X., Fractional Landweber iterative regularization method for identifying the unknown source of the time-fractional diffusion problem, Acta Applicandae Mathematicae, 175, 1 (2021) · Zbl 1476.35339 · doi:10.1007/s10440-021-00442-1 |
[22] |
Binh, T. T.; Nashine, H. K.; Le, D. L.; Nguyen, H. L.; Can, N., Identification of source term for the ill-posed Rayleigh-Stokes problem by Tikhonov regularization method, Advances in Difference Equations, 2019, 1 (2019) · Zbl 1485.35416 · doi:10.1186/s13662-019-2261-7 |
[23] |
Tuan, N. H.; Long, L. D.; Thinh, N. V., Regularized solution of an inverse source problem for a time fractional diffusion equation, Applied Mathematical Modelling, 40, 19-20, 8244-8264 (2016) · Zbl 1471.65124 · doi:10.1016/j.apm.2016.04.009 |
[24] |
Bakushinsky, A. B.; Kokurin, M. Y.; Smirnova, A., Iterative Methods for Ill-Posed Problems (2011), Inverse and Ill-Posed Problems Series · Zbl 1215.47013 |
[25] |
Louis, A. K., Inverse und Schlecht Gestellte Probleme (2013), Springer-Verlag |
[26] |
Can, N. H.; Luc, N. H.; Baleanu, D.; Zhou, Y., Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel, Advances in Difference Equations, 1 (2020) · Zbl 1482.35272 |
[27] |
Tuan, N. H.; O’regan, D.; Ngoc, T. B., Continuity with respect to fractional order of the time fractional diffusion-wave equation, Evolution Equations & Control Theory, 9, 3, 773-793 (2020) · Zbl 1455.35295 · doi:10.3934/eect.2020033 |