References
- Asogwa, S. A., Foondun, M., Mijena, J. B., Nane, E. (2020). Critical parameters for reaction–diffusion equations involving space–time fractional derivatives. Nonlinear Differ. Equ. Appl. 27(3):1–22. DOI: https://doi.org/10.1007/s00030-020-00629-9.
- Baeumer, B., Geissert, M., Kovács, M. (2015). Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise. J. Differ. Equ. 258(2):535–554. DOI: https://doi.org/10.1016/j.jde.2014.09.020.
- Caraballo, T., Colucci, R. (2017). A qualitative description of microstructure formation and coarsening phenomena for an evolution equation. Nonlinear Differ. Equ. Appl. 24(2):14. DOI: https://doi.org/10.1007/s00030-017-0437-y.
- Caraballo, T., Márquez-Durán, A. M. (2013). Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay. Dyn. Partial Differ. Equ. 10(3):267–281. DOI: https://doi.org/10.4310/DPDE.2013.v10.n3.a3.
- Chen, H., Xu, H. (2019). Global Existence, Exponential Decay and Blow-up in Finite Time for a Class of Finitely Degenerate Semilinear Parabolic Equations. Acta Math. Sci. 39(5):1290–1308. DOI: https://doi.org/10.1007/s10473-019-0508-8.
- Dang, D. T., Nane, E., Nguyen, D. M., Tuan, N. H. (2018). Continuity of solutions of a class of fractional equations. Potential Anal. 49(3):423–478. DOI: https://doi.org/10.1007/s11118-017-9663-5.
- Foondun, M., Nualart, E. (2014). On the behaviour of stochastic heat equations on bounded domains, arXiv preprint arXiv:1412.2343.
- Podlubny, I. (1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. New York, NY: Elsevier.
- PrévôT, C., Röckner, M. (2007). A Concise Course on Stochastic Partial Differential Equations (Vol. 1905, pp. vi+–144). Berlin, Germany: Springer.
- Samko, S. G., Kilbas, A. A., Marichev, O. I. (1993). Fractional Integrals and Derivatives, Theory and Applications. Yverdon, Switzerland: Gordon and Breach Science Publishers.
- Barenblat, G. I., Kochiva, I. (1960). Basic concepts in the theory of seepage of homogeneous liquids in fissured rock. J. Appl. Math. Mech. 24(5):1286–1303.
- Benjamin, T. B., Bona, J. L., Mahony, J. J. (1972). Model equations for long waves in nonlinear dispersive systems. Philos. Trans. Roy. Soc. London Ser. A. 272(1220):47–78.
- Ting, T. W. (1963). Certain non-steady flows of second-order fluids. Arch. Rational Mech. Anal. 14(1):1–26. DOI: https://doi.org/10.1007/BF00250690.
- Padron, V. (2004). Effect of aggregation on population recovery modeled by a forward-backward pseudoparabolic equation. Trans. Am. Math. Soc. 356(7):2739–2756.
- Cao, Y., Yin, J., Wang, C. (2009). Cauchy problems of semilinear pseudo-parabolic equations. J. Differ. Equ. 246(12):4568–4590. DOI: https://doi.org/10.1016/j.jde.2009.03.021.
- Cao, Y., Liu, C. (2018). Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. Electron. J. Diff. Equ. 116(2018):1–19.
- Caraballo, T., Duran, A.M.M., Rivero, F. (2015). Well-posedness and asymptotic behavior of a nonclassical nonautonomous diffusion equation with delay. Int. J. Bifurcation Chaos. 25(14):1540021. DOI: https://doi.org/10.1142/S0218127415400210.
- Caraballo, T., Duran, A.M.M., Rivero, F. (2017). Asymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristic. Discrete Contin. Dyn. Syst. Ser. B. 22(5):1817–1833.
- Chen, H., Tian, S. (2015). Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity. J. Differ. Equ. 258(12):4424–4442. DOI: https://doi.org/10.1016/j.jde.2015.01.038.
- Di, H., Shang, Y., Zheng, X. (2016). Global well-posedness for a fourth order pseudo-parabolic equation with memory and source terms. Discrete Contin. Dyn. Syst. Ser. B. 21(3):781–801. DOI: https://doi.org/10.3934/dcdsb.2016.21.781.
- Ding, H., Zhou, J. (2019). Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. J. Math. Anal. Appl. 478(2):393–420. DOI: https://doi.org/10.1016/j.jmaa.2019.05.018.
- He, Y., Gao, H., Wang, H. (2018). Blow-up and decay for a class of pseudo-parabolic p-Laplacian equation with logarithmic nonlinearity. Comput. Math. Appl. 75(2):459–469. DOI: https://doi.org/10.1016/j.camwa.2017.09.027.
- Jin, L., Li, L., Fang, S. (2017). The global existence and time-decay for the solutions of the fractional pseudo-parabolic equation. Comput. Math. Appl. 73(10):2221–2232. DOI: https://doi.org/10.1016/j.camwa.2017.03.005.
- Korpusov, M. O., Sveshnikov, A. G. (2004). Three-dimensional nonlinear evolutionary pseudoparabolic equations in mathematical physics. II Zh. Vychisl. Mat. Mat. Fiz. 44(11):2041–2048.
- Lu, Y., Fei, L. (2016). Bounds for blow-up time in a semilinear pseudo-parabolic equation with nonlocal source. J. Inequal. Appl. 2016(1):1–11. DOI: https://doi.org/10.1186/s13660-016-1171-4.
- Rao, V.R.G., Ting, T.W. (1972). Solutions of pseudo-heat equations in the whole space. Arch. Rational Mech. Anal. 49(1):57–78. DOI: https://doi.org/10.1007/BF00281474.
- Ting, T. W. (1969). Parabolic and pseudo-parabolic partial differential equations. J. Math. Soc. Japan. 21(3):440–453.
- Bai, L., Zhang, F.H. (2016). Existence of random attractors for 2D-stochastic nonclassical diffusion equations on unbounded domains. Results Math. 69(1–2):129–160. DOI: https://doi.org/10.1007/s00025-015-0505-8.
- Caraballo, T., Garrido-Atienza, M. J., Real, J. (2003). Stochastic stabilization of differential systems with general decay rate. Syst. Control Lett. 48(5):397–406. DOI: https://doi.org/10.1016/S0167-6911(02)00293-1.
- Liu, Z., Qiao, Z. (2020). Strong approximation of monotone stochastic partial differential equations driven by white noise. IMA J. Num. Anal. 40(2):1074–1093. DOI: https://doi.org/10.1093/imanum/dry088.
- Wang, R., Li, Y., Wang, B. (2020). Bi-spatial pullback attractors of fractional nonclassical diffusion equations on unbounded domains with (p, q)-growth nonlinearities. Appl. Math. Optim. 2020:1–37.
- Wang, R., Li, Y., Wang, B. (2019). Random dynamics of fractional nonclassical diffusion equations driven by colored noise. Discrete Cont. Dyn. Syst. A. 39(7):4091–4126. DOI: https://doi.org/10.3934/dcds.2019165.
- Wang, R., Shi, L., Wang, B. (2019). Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on RN. Nonlinearity. 32(11):4524–4556.
- Garrido-Atienza, M.J., Lu, K., Schmalfuss, B. (2010). Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete Contin. Dyn. Syst. Ser. B. 14(2):473–493. DOI: https://doi.org/10.3934/dcdsb.2010.14.473.
- Garrido-Atienza, M. J., Maslowski, B., Schmalfuß, B. (2010). Random attractors for stochastic equations driven by a fractional Brownian motion. Int. J. Bifurcation Chaos. 20(09):2761–2782. DOI: https://doi.org/10.1142/S0218127410027349.
- Grecksch, W., Anh, V.V. (1999). A parabolic stochastic differential equation with fractional Brownian motion input. Statist. Probab. Lett. 41(4):337–345. DOI: https://doi.org/10.1016/S0167-7152(98)00147-3.
- Gubinelli, M., Lejay, A., Tindel, S. (2006). Young integrals and SPDEs. Geom. Funct. Anal. 25(4):307–326.
- Li, Z., Yan, L. (2019). Stochastic averaging for two-time-scale stochastic partial differential equations with fractional Brownian motion. Nonlinear Anal. Hybrid Syst. 31:317–333. DOI: https://doi.org/10.1016/j.nahs.2018.10.002.
- Maslowski, B., Nualart, D. (2003). Evolution equations driven by a fractional Brownian motion. J. Funct. Anal. 202(1):277–305. DOI: https://doi.org/10.1016/S0022-1236(02)00065-4.
- Nualart, D., Raskanu, A. (2002). Differential equations driven by fractional Brownian motion. Collect. Math. 53(1):55–81.
- Tindel, S., Tudor, C., Viens, F. (2003). Stochastic evolution equations with fractional Brownian motion. Probab. Theory Relat. Fields. 127(2):186–204. DOI: https://doi.org/10.1007/s00440-003-0282-2.
- Atangana, A. (2018). Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology. London, UK: Academic Press.
- Ding, X. L., Nieto, J. J. (2018). Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms. Fract. Calc. Appl. Anal. 21(2):312–335. DOI: https://doi.org/10.1515/fca-2018-0019.
- Lax, P. D. (2002). Functional Analysis. New York, NY: Wiley Interscience.
- Srivastava, H.M., Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations. New York, NY: Elsevier.
- Zhou, Y., Wang, J., Zhang, L. (2016). Basic Theory of Fractional Differential Equations, Singapore: World Scientific.
- Foondun, M. (2018). Remarks on a fractional-time stochastic equation. arXiv preprint arXiv:1811.05391.
- Hu, G., Lou, Y., Christofides, P. D. (2008). Dynamic output feedback covariance control of stochastic dissipative partial differential equations. Chem. Eng. Sci. 63(18):4531–4542. DOI: https://doi.org/10.1016/j.ces.2008.06.026.
- Jiang, Y., Wei, T., Zhou, X. (2012). Stochastic generalized Burgers equations driven by fractional noises. J. Differ. Equ. 252(2):1934–1961. DOI: https://doi.org/10.1016/j.jde.2011.07.032.
- Kilbas, A. A., Srivastava, H. M., Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations (Vol. 204). New York, NY: Elsevier.
- Li, F., Li, Y., Wang, R. (2018). Regular measurable dynamics for reaction-diffusion equations on narrow domains with rough noise. Discrete Cont. Dyn. Syst. A. 38(7):3663–3685. DOI: https://doi.org/10.3934/dcds.2018158.
- Li, Y., Wang, Y. (2019). The existence and asymptotic behavior of solutions to fractional stochastic evolution equations with infinite delay. J. Differ. Equ. 266(6):3514–3558. DOI: https://doi.org/10.1016/j.jde.2018.09.009.
- Pedjeu, J. C., Ladde, G. S. (2012). Stochastic fractional differential equations: Modeling, method and analysis. Chaos Solitons Fractals. 45(3):279–293. DOI: https://doi.org/10.1016/j.chaos.2011.12.009.
- Su, X., Li, M. (2018). The regularity of fractional stochastic evolution equations in Hilbert space. Stoch. Anal. Appl. 36(4):639–653. DOI: https://doi.org/10.1080/07362994.2018.1436973.
- Zou, G. A., Wang, B. (2017). Stochastic Burgers’ equation with fractional derivative driven by multiplicative noise. Comput. Math. Appl. 74(12):3195–3208. DOI: https://doi.org/10.1016/j.camwa.2017.08.023.
- Zou, G. A., Wang, B., Zhou, Y. (2018). Existence and regularity of mild solutions to fractional stochastic evolution equations. Math. Model. Nat. Phenom. 13(1):15. DOI: https://doi.org/10.1051/mmnp/2018004.
- Biagini, F., Hu, Y., Øksendal, B., Zhang, T. (2008). Stochastic Calculus for Fractional Brownian Motion and Applications. Probability and Its Applications (New York). London, UK: Springer-Verlag London, Ltd., pp. xii+–329. pp. ISBN: 978-1-85233-996-8.
- de la Fuente, I. M., Perez-Samartin, A. L., Martínez, L., Garcia, M. A., Vera-Lopez, A. (2006). Long-range correlations in rabbit brain neural activity. Ann. Biomed. Eng. 34(2):295–299. DOI: https://doi.org/10.1007/s10439-005-9026-z.
- Mishura, Y.S. (2008). Stochastic Calculus for Fractional Brownian Motion and Related Processes. Berlin, Germany: Springer-Verlag.
- Rypdal, M., Rypdal, K. (2010). Testing hypotheses about sun-climate complexity linking. Phys. Rev. Lett. 104(12):128501. DOI: https://doi.org/10.1103/PhysRevLett.104.128501.
- Simonsen, I. (2003). Measuring anti-correlations in the nordic electricity spot market by wavelets. Physics. A322:597–606.
- Beshtokov, M. K. (2018). To boundary-value problems for degenerating pseudoparabolic equations with Gerasimov–Caputo fractional derivative. Russ. Math. 62(10):1–14. DOI: https://doi.org/10.3103/S1066369X18100018.
- Beshtokov, M. K. (2019). Boundary-value problems for loaded pseudoparabolic equations of fractional order and difference methods of their solving. Russ. Math. 63(2):1–10. DOI: https://doi.org/10.3103/S1066369X19020014.
- Beshtokov, M. K. (2019). Boundary Value Problems for a Pseudoparabolic Equation with the Caputo Fractional Derivative. Diff. Equat. 55(7):884–893. DOI: https://doi.org/10.1134/S0012266119070024.
- Sousa, J. V. D. C., de Oliveira, E. C. (2019). Fractional order pseudoparabolic partial differential equation: Ulam–Hyers stability. Bull. Braz. Math. Soc. New Series. 50(2):481–496. DOI: https://doi.org/10.1007/s00574-018-0112-x.
- Van Au, V., Jafari, H., Hammouch, Z., Tuan, N. H. (2019). On a final value problem for a nonlinear fractional pseudo-parabolic equation, Electronic Research Archive.
- Arendt, W., Ter Elst, A. F., Warma, M. (2018). Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator. Commun. Part. Diff. Eq. 43(1):1–24. DOI: https://doi.org/10.1080/03605302.2017.1363229.
- Debbi, L. (2016). Well-posedness of the multidimensional fractional stochastic Navier–Stokes equations on the torus and on bounded domains. J. Math. Fluid Mech. 18(1):25–69. DOI: https://doi.org/10.1007/s00021-015-0234-5.
- Kato, T. (2013). Perturbation Theory for Linear Operators (Vol. 132). Berlin, Germany: Springer Science & Business Media.
- Nualart, D. (2006). The Malliavin Calculus and Related Topics. 2nd ed. Berlin, Germany: Springer-Verlag.