Abstract
In the present work, a modified numerical model was developed to simulate the water flow during a dam break with the mud layer transfer of different heights, consisting of three phases (water, air, and a phase for deposition). To carry out a numerical simulation of this process, a mathematical model based on the VOF (volume of fluid) method was modified, taking into account the movement of the water-free surface, which is carried out by the movement of water flow based on the Newtonian fluid model, and the movement of mud impurities is based on the non-Newtonian fluid model. Validation of the constructed model for the influence of three-dimensional features of the flow on morphological changes is carried out by a modified mathematical model and compared with the results of calculation for two-dimensional (2D) and three-dimensional (3D) models. The proposed method for modeling is applied on a real complex terrain, which was based on the Kargalinka – a river in Almaty and the Almaty region of Kazakhstan, the right tributary of the Kaskelen River. Simulation analysis is carried out for cases with different deposit heights. All results of the numerical simulation can be visually viewed using graphs and illustrations.
-
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: This work is supported by the grant from the Ministry of education and science of the Republic of Kazakhstan (AP09058406).
-
Conflict of interest statement: The authors declare that there is no conflict of interests regarding the publication of this paper.
-
Availability of data and materials: The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
[1] R. Marsooli and W. Wu, “Three-dimensional numerical modeling of dam-break flows with sediment transport over movable beds,” J. Hydraul. Eng., vol. 141, no. 1, p. 04014066, 2015. https://doi.org/10.1061/(asce)hy.1943-7900.0000947.Suche in Google Scholar
[2] V. Naderkhanloo, M. Soudi, and M. Hemmati, “3D numerical simulation of dam-break flows with sediment transport over movable beds,” in World Environmental and Water Resources Congress 2017: International Perspectives, History and Heritage, Emerging Technologies, and Student Papers, 2017, pp. 161–170.10.1061/9780784480595.015Suche in Google Scholar
[3] R. Marsooli and W. Wu, “3-D finite-volume model of dam-break flow over uneven beds based on VOF method,” Adv. Water Resour., vol. 70, pp. 104–117, 2014. https://doi.org/10.1016/j.advwatres.2014.04.020.Suche in Google Scholar
[4] S. Soares-Frazao, R. Canelas, and Z. Cao, “Dam-break flows over mobile beds: experiments and benchmark tests for numerical models,” J. Hydraul. Res., vol. 50, no. 4, pp. 364–375, 2012. https://doi.org/10.1080/00221686.2012.689682.Suche in Google Scholar
[5] K. M. T. Kleefsman, G. Fekken, and A. E. P. Veldman, “A Volume-of-fluid based simulation method for wave impact problems,” J. Comput. Phys., vol. 206, no. 1, pp. 363–393, 2005. https://doi.org/10.1016/j.jcp.2004.12.007.Suche in Google Scholar
[6] B. Spinewine and Y. Zech, “Small-scale laboratory dam-break waves on movable beds,” J. Hydraul. Res., vol. 45, pp. 73–86, 2007. https://doi.org/10.1080/00221686.2007.9521834.Suche in Google Scholar
[7] M. Zhang, Y. Xu, and Z. Hao, “Integrating 1D and 2D hydrodynamic, sediment transport model for dam-break flow using finite volume method,” Sci. China Phys. Mech. Astron., vol. 57, no. 4, pp. 774–783, 2014. https://doi.org/10.1007/s11433-013-5294-z.Suche in Google Scholar
[8] W. Wu, R. Marsooli, and Z. He, “Depth-averaged two-dimensional model of unsteady flow and sediment transport due to noncohesive embankment break/breaching,” J. Hydraul. Eng., vol. 138, no. 6, pp. 503–516, 2012. https://doi.org/10.1061/(asce)hy.1943-7900.0000546.Suche in Google Scholar
[9] L. A. LaRocque, J. Imran, and M. H. Chaudhry, “Experimental and numerical investigations of two-dimensional dam-break flows,” J. Hydraul. Eng., vol. 139, no. 6, pp. 569–579, 2013. https://doi.org/10.1061/(asce)hy.1943-7900.0000705.Suche in Google Scholar
[10] Y. Zech, S. Soares-Frazao, and B. Spinewine, “Dam-break induced sediment movement: experimental approaches and numerical modelling,” J. Hydraul. Res., vol. 46, no. 2, pp. 176–190, 2008. https://doi.org/10.1080/00221686.2008.9521854.Suche in Google Scholar
[11] P. Costabile and E. Macchione, “One dimensional modeling of dam break flow over erodible sediment bed,” in International Conference on Fluvial Hydraulics, RIVER FLOW 2006, 2006, p. 1501.10.1201/9781439833865.ch160Suche in Google Scholar
[12] Z. Yue, Z. Fu, and H. Liu, “Well-balanced 2D coupled modelling of dam-break sediment-laden flood processes in a real river channel,” in 35th World Congress of the International-Association-for-Hydro-Environment-Engineering-and-Research (IAHR), 2013.Suche in Google Scholar
[13] P. Lin, Y. Wu, and J. Bai, “A Numerical study of dam-break flow and sediment transport from a quake lake,” J. Earthq. Tsunami, vol. 5, no. 5, pp. 401–428, 2011. https://doi.org/10.1142/s1793431111001169.Suche in Google Scholar
[14] L. Fu and Y. C. Jin, “Improved multiphase Lagrangian method for simulating sediment transport in dam-break flows,” J. Hydraul. Eng., vol. 142, no. 6, p. 04016005, 2016. https://doi.org/10.1061/(asce)hy.1943-7900.0001132.Suche in Google Scholar
[15] F. Benkhaldoun, S. Sari, and M. Seaid, “A flux-limiter method for dam-break flows over erodible sediment beds,” Appl. Math. Model., vol. 36, no. 10, pp. 4847–4861, 2012. https://doi.org/10.1016/j.apm.2011.11.088.Suche in Google Scholar
[16] C. H. Yu, H. L. Wen, and Z. H. Gu, “Numerical simulation of dam-break flow impacting a stationary obstacle by a CLSVOF/IB method,” Commun. Nonlinear Sci. Numer. Simulat., vol. 79, pp. 1–39, 2019. https://doi.org/10.1016/j.cnsns.2019.104934.Suche in Google Scholar
[17] Z. H. Gu, H. L. Wen, and C. H. Yu, “Interface-preserving level set method for simulating dam-break flows,” J. Comput. Phys., vol. 374, pp. 249–280, 2018. https://doi.org/10.1016/j.jcp.2018.07.057.Suche in Google Scholar
[18] M. Zhang and W. M. Wu, “A two dimensional hydrodynamic and sediment transport model for dam break based on finite volume method with quadtree grid,” Appl. Ocean Res., vol. 33, no. 4, pp. 297–308, 2011. https://doi.org/10.1016/j.apor.2011.07.004.Suche in Google Scholar
[19] T. R. Wu, V. Thi-Hong-Nhi, and J. W. Lin, “Three-dimensional numerical study on the interaction between dam-break wave and cylinder array,” J. Earthq. Tsunami, vol. 12, no. 2, p. 1840007, 2018. https://doi.org/10.1142/s1793431118400079.Suche in Google Scholar
[20] Y. Ozeren, R. Aleixo, and M. Altinakar, “Laboratory experiments on dam-break flow of water-sediment mixtures,” in 7th International Conference on Fluvial Hydraulics (River Flow), River flow, 2014, pp. 1639–1646.10.1201/b17133-218Suche in Google Scholar
[21] A. Issakhov, Y. Zhandaulet, and A. Nogaeva, “Numerical simulation of dam break flow for various forms of the obstacle by VOF method,” Int. J. Multiphas. Flow, vol. 109, pp. 191–206, 2018. https://doi.org/10.1016/j.ijmultiphaseflow.2018.08.003.Suche in Google Scholar
[22] A. Issakhov and M. Imanberdiyeva, “Numerical simulation of the movement of water surface of dam break flow by VOF methods for various obstacles,” Int. J. Heat Mass Tran., vol. 136, pp. 1030–1051, 2019. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.034.Suche in Google Scholar
[23] A. Issakhov and A. Borsikbayeva, “The impact of a multilevel protection column on the propagation of a water wave and pressure distribution during a dam break: numerical simulation,” J. Hydrol., vol. 598, p. 126212, 2021. https://doi.org/10.1016/j.jhydrol.2021.126212.Suche in Google Scholar
[24] E. Lakzian and A. Estiri, “Entropy generation analysis as design criteria in dam-break flows for non-Newtonian fluids,” Eur. Phys. J. Plus, vol. 133, no. 11, p. 454, 2018. https://doi.org/10.1140/epjp/i2018-12259-7.Suche in Google Scholar
[25] G. Wu, Z. Yang, and K. Zhang, “A non-equilibrium sediment transport model for dam break flow over moveable bed based on non-uniform rectangular mesh,” Water, vol. 10, no. 5, p. 616, 2018. https://doi.org/10.3390/w10050616.Suche in Google Scholar
[26] W. Lai and A. A. Khan, “Modeling dam-break flood over natural rivers using discontinuous Galerkin method,” J. Hydrodyn., vol. 24, no. 4, pp. 467–478, 2012. https://doi.org/10.1016/s1001-6058(11)60268-0.Suche in Google Scholar
[27] B. Yu-chuan, D. Xu, and L. Dong-qiang, “Numerical simulation of two-dimensional dam-break flows in curved channels,” J. Hydrodyn., vol. 19, no. 6, pp. 726–735, 2007. https://doi.org/10.1016/s1001-6058(08)60010-4.Suche in Google Scholar
[28] S. K. Biswal, M. K. Moharana, and A. K. Agrawal, “Effects of initial stage of dam-break flows on sediment transport,” Sadhana Acad. Proc. Eng. Sci., vol. 43, no. 12, p. 203, 2018. https://doi.org/10.1007/s12046-018-0968-x.Suche in Google Scholar
[29] H. Capart and D. L. Young, “Formation of a jump by the dam-break wave over a granular bed,” J. Fluid Mech., vol. 372, pp. 165–187, 1998. https://doi.org/10.1017/s0022112098002250.Suche in Google Scholar
[30] H. Capart, D. L. Young, and Y. Zech, “Dam-break induced debris flow,” Particulate Gravity Currents, vol. 31, pp. 149–156, 2001. https://doi.org/10.1002/9781444304275.ch11.Suche in Google Scholar
[31] L. Guertault, B. Camenen, and C. Peteuil, “One-dimensional modeling of suspended sediment dynamics in dam reservoirs,” J. Hydraul. Eng., vol. 142, no. 10, p. 04016033, 2016. https://doi.org/10.1061/(asce)hy.1943-7900.0001157.Suche in Google Scholar
[32] l. Fraccarollo and H. Capart, “Riemann wave description of erosional dam-break flows,” J. Fluid Mech., vol. 461, pp. 183–228, 2002. https://doi.org/10.1017/s0022112002008455.Suche in Google Scholar
[33] P. Z. Lin and P. L. F. Liu, “A numerical study of breaking waves in the surf zone,” J. Fluid Mech., vol. 359, pp. 239–264, 1998. https://doi.org/10.1017/s002211209700846x.Suche in Google Scholar
[34] P. Z. Lin and P. L. F. Liu, “Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone,” J. Geophys. Res., vol. 103, no. C8, pp. 15677–15694, 1998. https://doi.org/10.1029/98jc01360.Suche in Google Scholar
[35] H.-C. Hsu, A. Torres-Freyermuth, T.-J. Hsu, H.-H. Hwung, and P.-C. Kuo, “On dam-break wave propagation and its implication to sediment erosion,” J. Hydraul. Res., vol. 52, no. 2, pp. 205–218, 2014. https://doi.org/10.1080/00221686.2013.857365.Suche in Google Scholar
[36] Z. Cao, G. Pender, S. Wallis, and P. Carling, “Computational dam-break hydraulics over erodible sediment bed,” J. Hydraul. Eng., vol. 130, no. 7, pp. 689–703, 2004. https://doi.org/10.1061/(asce)0733-9429(2004)130:7(689).10.1061/(ASCE)0733-9429(2004)130:7(689)Suche in Google Scholar
[37] J. J. Monaghan, “Smoothed particle hydrodynamics and its diverse applications,” Annu. Rev. Fluid Mech., vol. 44, pp. 323–346, 2012. https://doi.org/10.1146/annurev-fluid-120710-101220.Suche in Google Scholar
[38] X. Xu, “An improved SPH approach for simulating 3D dam-break flows with breaking waves,” Comput. Methods Appl. Mech. Eng., vol. 311, pp. 723–742, 2016. https://doi.org/10.1016/j.cma.2016.09.002.Suche in Google Scholar
[39] X. Xu, Y. L. Jiang, and P. Yu, “SPH simulations of 3D dam-break flow against various forms of the obstacle: toward an optimal design,” Ocean Eng., vol. 229, p. 108978, 2021. https://doi.org/10.1016/j.oceaneng.2021.108978.Suche in Google Scholar
[40] I. K. Nikolos and A. I. Delis, “An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography,” Comput. Methods Appl. Mech. Eng., vol. 198, nos. 47–48, pp. 3723–3750, 2009. https://doi.org/10.1016/j.cma.2009.08.006.Suche in Google Scholar
[41] C. Di Cristo, S. Evangelista, M. Greco, M. Iervolino, A. Leopardi, and A. Vacca, “Dam-break waves over an erodible embankment: experiments and simulations,” J. Hydraul. Res., vol. 56, no. 2, pp. 196–210, 2018. https://doi.org/10.1080/00221686.2017.1313322.Suche in Google Scholar
[42] S. Evangelista, M. S. Altinakar, C. Di Cristo, and A. Leopardi, “Simulation of dam-break waves on movable beds using a multi-stage centered scheme,” Int. J. Sediment Res., vol. 28, no. 3, pp. 269–284, 2013. https://doi.org/10.1016/s1001-6279(13)60039-6.Suche in Google Scholar
[43] Y. Cui, G. Parker, J. Pizzuto, and T. E. Lisle, “Sediment pulses in mountain rivers: 2. Comparison between experiments and numerical predictions,” Water Resour. Res., vol. 39, no. 9, pp. 1240–1251, 2003. https://doi.org/10.1029/2002wr001805.Suche in Google Scholar
[44] W. Wu, D. A. Vieira, and S. S. Wang, “One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks,” J. Hydraul. Eng., vol. 130, no. 9, pp. 914–923, 2004. https://doi.org/10.1061/(asce)0733-9429(2004)130:9(914).10.1061/(ASCE)0733-9429(2004)130:9(914)Suche in Google Scholar
[45] L. Goutière, S. Soares-Frazão, C. Savary, T. Laraichi, and Y. Zech, “One-dimensional model for transient flows involving bed-load sediment transport and changes in flow regimes,” J. Hydraul. Eng., vol. 134, no. 6, pp. 726–735, 2008. https://doi.org/10.1061/(asce)0733-9429(2008)134:6(726).10.1061/(ASCE)0733-9429(2008)134:6(726)Suche in Google Scholar
[46] R. I. Ferguson, M. Church, C. D. Rennie, and J. G. Venditti, “Reconstructing a sediment pulse: modeling the effect of placer mining on Fraser river, Canada,” J. Geophys. Res. Solid Earth, vol. 120, no. 7, pp. 1436–1454, 2015. https://doi.org/10.1002/2015jf003491.Suche in Google Scholar
[47] F. Carraro, A. Valiani, and V. Caleffi, “Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant–Exner morphodynamic model,” Adv. Water Resour., vol. 113, pp. 189–201, 2018. https://doi.org/10.1016/j.advwatres.2018.01.011.Suche in Google Scholar
[48] W. Wu and S. S. Wang, “One-dimensional modeling of dam-break flow over movable beds,” J. Hydraul. Eng., vol. 133, no. 1, pp. 48–58, 2007. https://doi.org/10.1061/(asce)0733-9429(2007)133:1(48).10.1061/(ASCE)0733-9429(2007)133:1(48)Suche in Google Scholar
[49] L. Liang, X. Yu, and F. Bombardelli, “A general mixture model for sediment laden flows,” Adv. Water Resour., vol. 107, pp. 108–125, 2017. https://doi.org/10.1016/j.advwatres.2017.06.012.Suche in Google Scholar
[50] C. Juez, J. Murillo, and P. García-Navarro, “A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed,” Adv. Water Resour., vol. 71, pp. 93–109, 2014. https://doi.org/10.1016/j.advwatres.2014.05.014.Suche in Google Scholar
[51] F. N. Cantero-Chinchilla, O. Castro-Orgaz, S. Dey, and J. L. Ayuso-Muñoz, “Nonhydrostatic dam break flows. II: one-dimensional depth-averaged modeling for mov- able bed flows,” J. Hydraul. Eng., vol. 142, no. 12, p. 04016069, 2016. https://doi.org/10.1061/(asce)hy.1943-7900.0001206.Suche in Google Scholar
[52] G. Chambon, A. Ghemmour, and D. Laigle, “Gravity-driven surges of a viscoplastic fluid: an experimental study,” J. Non-Newtonian Fluid Mech., vol. 158, nos. 1–3, pp. 54–62, 2009. https://doi.org/10.1016/j.jnnfm.2008.08.006.Suche in Google Scholar
[53] C. Ancey and S. Cochard, “The dam-break problem for Herschel-Bulkley viscoplastic fluids down steep flumes,” J. Non-Newtonian Fluid Mech., vol. 158, nos. 1–3, pp. 18–35, 2009. https://doi.org/10.1016/j.jnnfm.2008.08.008.Suche in Google Scholar
[54] X. Li and J. Zhao, “Dam-break of mixtures consisting of non-Newtonian liquids and granular particles,” Powder Technol., vol. 338, pp. 493–505, 2018. https://doi.org/10.1016/j.powtec.2018.07.021.Suche in Google Scholar
[55] C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys., vol. 39, no. 1, pp. 201–225, 1981. https://doi.org/10.1016/0021-9991(81)90145-5.Suche in Google Scholar
[56] A. Liu, A. Xiong, and X. Liu, “Numerical simulations of dam-break flow on complicated terrain using VOF method,” in International Conference on Mechanical and Automation Engineering, 2013, pp. 229–232.10.1109/MAEE.2013.64Suche in Google Scholar
[57] R. I. Issa, “Solution of the implicitly discretized fluid flow equations by operator splitting,” J. Comput. Phys., vol. 62, no. 1, pp. 40–65, 1986. https://doi.org/10.1016/0021-9991(86)90099-9.Suche in Google Scholar
[58] A. Issakhov, A. Alimbek, and Y. Zhandaulet, “The assessment of water pollution by chemical reaction products from the activities of industrial facilities: numerical study,” J. Clean. Prod., vol. 282, p. 125239, 2021. https://doi.org/10.1016/j.jclepro.2020.125239.Suche in Google Scholar
[59] A. Issakhov and P. Omarova, “Modeling and analysis of the effects of barrier height on automobiles emission dispersion,” J. Clean. Prod., vol. 296, p. 126450, 2021. https://doi.org/10.1016/j.jclepro.2021.126450.Suche in Google Scholar
[60] A. Issakhov, A. Alimbek, and A. Issakhov, “A numerical study for the assessment of air pollutant dispersion with chemical reactions from a thermal power plant,” Eng. Appl. Comp. Fluid Mech., vol. 14, no. 1, pp. 1035–1061, 2020. https://doi.org/10.1080/19942060.2020.1800515.Suche in Google Scholar
[61] A. Issakhov, A. Abylkassymova, and A. Issakhov, “Assessment of the influence of the barriers height and trees with porosity properties on the dispersion of emissions from vehicles in a residential area with various types of building developments,” J. Cleaner Prod., vol. 366, p. 132581, 2022. https://doi.org/10.1016/j.jclepro.2022.132581.Suche in Google Scholar
[62] A. Issakhov, A. Tursynzhanova, and A. Abylkassymova, “Numerical study of air pollution exposure in idealized urban street canyons: Porous and solid barriers,” Urban Climate, vol. 43, p. 101112, 2022. https://doi.org/10.1016/j.uclim.2022.101112.Suche in Google Scholar
[63] A. Issakhov and P. Omarova, “Numerical simulation of pollutant dispersion in the residential areas with continuous grass barriers,” Int. J. Environ. Sci. Technol., vol. 17, no. 1, pp. 525–540, 2020.10.1007/s13762-019-02517-xSuche in Google Scholar
[64] A. Issakhov,A. Alimbek, and A. Abylkassymova, “Numerical modeling of water pollution by products of chemical reactions from the activities of industrial facilities at variable and constant temperatures of the environment,” J. Cont. Hydrol., vol. 104116, p. 104116, 2022. https://doi.org/10.1016/j.jconhyd.2022.104116.Suche in Google Scholar
[65] I. E. Barton, “Comparison of SIMPLE and PISO type algorithms for transient flows,” Int. J. Numer. Methods Fluid., vol. 26, no. 4, pp. 459–483, 1998. https://doi.org/10.1002/(sici)1097-0363(19980228)26:4<459::aid-fld645>3.0.co;2-u.10.1002/(SICI)1097-0363(19980228)26:4<459::AID-FLD645>3.0.CO;2-USuche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Article
- Hybrid solitary wave solutions of the Camassa–Holm equation
- Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
- A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
- Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
- Numerical modeling of the dam-break flood over natural rivers on movable beds
- A class of piecewise fractional functional differential equations with impulsive
- Lie symmetry analysis for two-phase flow with mass transfer
- Asymptotic behavior for stochastic plate equations with memory in unbounded domains
- Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
- A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
- Ground state solutions of Schrödinger system with fractional p-Laplacian
- Bifurcation analysis of a new stochastic traffic flow model
- An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
- Hilfer fractional stochastic evolution equations on infinite interval
- Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
- Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
- Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
- Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
- Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
- Shehu transform on time-fractional Schrödinger equations – an analytical approach
- A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
- Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
Artikel in diesem Heft
- Frontmatter
- Original Research Article
- Hybrid solitary wave solutions of the Camassa–Holm equation
- Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
- A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
- Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
- Numerical modeling of the dam-break flood over natural rivers on movable beds
- A class of piecewise fractional functional differential equations with impulsive
- Lie symmetry analysis for two-phase flow with mass transfer
- Asymptotic behavior for stochastic plate equations with memory in unbounded domains
- Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
- A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
- Ground state solutions of Schrödinger system with fractional p-Laplacian
- Bifurcation analysis of a new stochastic traffic flow model
- An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
- Hilfer fractional stochastic evolution equations on infinite interval
- Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
- Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
- Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
- Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
- Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
- Shehu transform on time-fractional Schrödinger equations – an analytical approach
- A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
- Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary