[1] Saffman, P.G., On the stability of laminar flow of a dusty gas, Journal of Fluid Mechanics, 13(1), 1962, 120–128.
[2] Kumar, P., Stability of superposed viscous–viscoelastic (Rivlin–Ericksen) fluids in the presence of suspended particles through a porous medium, Zeitschrift für angewandte Mathematik und Physik ZAMP, 51, 2000, 912–921.
[3] El-Sayed, M.F., Hydromagnetic instability of fluid–particle Kelvin–Helmholtz flow in Oldroydian viscoelastic porous media, Journal of Porous Media, 10(5), 2007, 443–458.
[4] Kumar, S., Rani, S., Symmetries of optimal system, closed-form solutions, and wave propagation for the Boussinesq–Burgers system in ocean waves, Physics of Fluids, 34, 2022, 037109.
[5] Rani, S., Dhiman, S.K., Kumar, S., Closed-form soliton solutions and modulation instability for a (2+1)-D cubic nonlinear Schrödinger equation using Lie subalgebra, Optical and Quantum Electronics, 56(4), 2024, 532.
[6] Islam, S.M.R., Arafat, S.M.Y., Wang, H., Closed-form wave solutions to the simplified modified Camassa–Holm equation, Journal of Ocean Engineering and Science, 8(3), 2023, 238–245.
[7] Kumar, S., Rani, S., Invariance analysis and closed-form solutions for a (2+1)-D dissipative long-wave system, Physica Scripta, 96(12), 2021, 125202.
[8] Kumar, S., Rani, S., Lie symmetry reductions and soliton dynamics of the (2+1)-D Pavlov equation, Pramana – Journal of Physics, 94, 2020, 116.
[9] Kumar, S., Kumar, A., Nonlinear extended Zakharov–Kuznetsov equation in (3+1) dimensions: solitary-wave solutions, Modern Physics Letters B, 36(25), 2022, 2250140.
[10] Pandey, A., Kumar, A., Tripathi, D., Sharma, K., Membrane-driven flow and heat transfer of viscoelastic fluids: MHD and entropy generation analysis, International Journal of Numerical Methods for Heat & Fluid Flow, 35(8), 2025, 2813–2840.
[11] Arshad, M., Hassan, A., Numerical investigation of viscoelastic nanofluid flow through a rotating non-Darcy porous medium with variable thermal conductivity, Facta Universitatis – Series Mechanical Engineering, 23(1), 2025, 112–134.
[12] Saleem, S., Nawaz, M., Finite element analysis of magnetohydrodynamic (MHD) viscoelastic fluid flow in chemically reactive porous media, Facta Universitatis – Series Mechanical Engineering, 22(3), 2024, 455–472.
[13] Kabeel, A.E., El-Said, E.M.S., Dafea, S.A., Magnetic-field effects on heat transfer in liquids, Renewable and Sustainable Energy Reviews, 45, 2015, 830–837.
[14] Melcher, J.R., Field Coupled Surface Waves, MIT Press, Cambridge, MA, 1963.
[15] Yang, J., Well-posedness of electrohydrodynamic waves under a vertical electric field, Zeitschrift für angewandte Mathematik und Physik ZAMP, 71, 2020, 20.
[16] Nayfeh, A.H., Mook, D.T., Nonlinear Oscillations, Wiley, New York, 1979.
[17] He, J.H., Analytical methods for nonlinear oscillators and fractional oscillators, Journal of Low Frequency Noise, Vibration and Active Control, 38(3–4), 2019, 1252–1260.
[18] El-Dib, Y.O., Elgazery, N.S., Alyousef, H.A., Upgrading rank approach for solving fractal Duffing oscillator, Facta Universitatis – Series Mechanical Engineering, 22(2), 2024, 199–216.
[19] El-Dib, Y.O., An innovative efficient approach to solving damped Mathieu–Duffing equation with the non-perturbative technique, Communications in Nonlinear Science and Numerical Simulation, 128, 2024, 107590.
[20] El-Dib, Y.O., Alyousef, H.A., An innovative solution to the Mathieu–Van der Pol–Helmholtz–Duffing equation, Chinese Journal of Physics, 95, 2025, 902–918.
[21] El-Dib, Y.O., Mady, A.A., Alyousef, H.A., Interfacial stability control of MHD Bingham fluids in micro-porous MEMS structures via fractal analysis, Frontiers in Physics, 13, 2025, 1634769.
[22] El-Dib, Y.O., Al-Ghamdi, H., Renormalization method for variable stiffness in fractal 2DOF nonlinear parametric oscillators, Journal of Vibration Engineering & Technologies, 13, 2025, 550.
[23] Rosensweig, R.E., Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985.
[24] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961.
[25] Shliomis, M.I., Magnetic fluids, Soviet Physics Uspekhi, 17(2), 1974, 153–169.
[26] Adrian, R.J., Particle-imaging techniques for experimental fluid mechanics, Annual Review of Fluid Mechanics, 23(1), 1991, 261–304.
[27] Mahr, T., Rehberg, I., Nonlinear dynamics of a single ferrofluid peak in an oscillating magnetic field, Physica D, 111(1–4), 1998, 335–346.
[28] Odenbach, S., Magnetoviscous Effects in Ferrofluids, Springer, 2002.
[29] Farge, M., Wavelet transforms and their applications to turbulence, Annual Review of Fluid Mechanics, 24(1), 1992, 395–457.
[30] Larson, R.G., The Structure and Rheology of Complex Fluids, Oxford University Press, 1999.
[31] Müller, H.W., Liu, M., Structure of ferrofluid dynamics, Physical Review E, 64(6), 2001, 061405.
[32] Berkovsky, B.M., Medvedev, V.F., Krakov, M.S., Magnetic Fluids: Engineering Applications, Oxford University Press, 1993.
[33] Carlson, J.D., Jolly, M.R., MR fluid, foam and elastomer devices, Mechatronics, 10(4–5), 2000, 555–569.
[34] Spencer, B.F., Nagarajaiah, S., State of the art of structural control, Journal of Structural Engineering, 129(7), 2003, 845–856.
[35] Jolly, M.R., Bender, J.W., Carlson, J.D., Properties and applications of commercial magnetorheological fluids, Journal of Intelligent Material Systems and Structures, 10(1), 1999, 5–13.
[36] Rabinow, J., The magnetic fluid clutch, AIEE Transactions, 67(2), 1948, 1308–1315.
[37] Pamme, N., Magnetism and microfluidics, Lab on a Chip, 6(1), 2006, 24–38.
[38] Whitesides, G.M., The origins and the future of microfluidics, Nature, 442(7101), 2006, 368–373.
[39] Lakes, R.S., Viscoelastic Solids, CRC Press, 1999.
[40] Pankhurst, Q.A., Connolly, J., Jones, S.K., Dobson, J., Applications of magnetic nanoparticles in biomedicine, Journal of Physics D: Applied Physics, 36(13), 2003, R167–R181.
[41] Lubbe, A.S., Bergemann, C., Brock, J., McClure, D.G., Physiological aspects in magnetic drug-targeting, Journal of Magnetism and Magnetic Materials, 194(1–3), 1999, 149–155.
[42] Rajagopal, K.R., Tao, L., Mechanics of Mixtures, World Scientific, 1995.
[43] Singh, M., Gupta, R.K., Double-diffusive convection in compressible Rivlin–Ericksen fluid with dust, Journal of Fluids, 2014, 2014, 714150.
[44] Funada, T., Joseph, D.D., Viscous potential flow analysis of Kelvin–Helmholtz instability, Journal of Fluid Mechanics, 445, 2001, 263–283.
[45] Funada, T., Joseph, D.D., Viscous potential flow analysis of capillary instability, International Journal of Multiphase Flow, 28(9), 2002, 1459–1478.
[46] Funada, T., Joseph, D.D., Viscoelastic potential flow analysis of capillary instability, Journal of Non-Newtonian Fluid Mechanics, 111(2–3), 2003, 87–105.
[47] Batchelor, G.K., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1997.
[48] Sharma, R.C., Sharma, N.D., Instability of streaming fluids with fine dust in porous media, Czechoslovak Journal of Physics, 42(9), 1992, 907–918.
[49] El-Dib, Y.O., Fractal-space features in nonlinear electrohydrodynamic Rayleigh–Taylor instability, Physics of Fluids, 36, 2024, 122127.
[50] Nordström, J., Laurén, F., Nonlinear interface coupling for incompressible Euler equations, Applied Mathematics Letters, 132, 2022, 108171.
[51] Nordström, J., Nonlinear boundary conditions for CFD initial–boundary value problems, Journal of Computational Physics, 498, 2024, 112685.
[52] Roe, B., Jaiman, R., Haselbacher, A., Geubelle, P.H., Combined interface boundary-condition method for coupled thermal simulations, International Journal for Numerical Methods in Fluids, 57(3), 2008, 329–354.
[53] Harrison, W.J., The influence of viscosity on the oscillations of superposed fluids, Proceedings of the London Mathematical Society, 6, 1908, 396.
[54] El-Dib, Y.O., Insights into transferal to fractal space modeling: delayed forced Helmholtz–Duffing oscillator with the non-perturbative approach, Communications in Theoretical Physics, 77, 2025, 015002.
[55] El-Dib, Y.O., Stability analysis for nonlinear Mathieu equation without perturbation, ZAMM – Journal of Applied Mathematics and Mechanics, 104(9), 2024, e202400047.
[56] Zhai, X., Linear stability of the Couette flow for non-isentropic compressible fluids, Electronic Journal of Differential Equations, 2025, 107.
[57] Spanos, P.T.D., Iwan, W.D., Existence and uniqueness of equivalent-linearization solutions, International Journal of Non-Linear Mechanics, 13(2), 1979, 71–78.
[58] El-Dib, Y.O., Masking technique for forced nonlinear oscillator stability, Journal of Low Frequency Noise, Vibration and Active Control, 43(4), 2024, 1481–1497.
[59] Cole, J.D., Perturbation Methods in Applied Mathematics, Blaisdell, 1968.
[60] McLachlan, N.W., Theory and Application of Mathieu Functions, Oxford University Press, 1947.
[61] Jordan, D., Smith, P., Ordinary Nonlinear Differential Equations, Oxford University Press, 2007.
[62] Landau, L.D., Lifshitz, E.M., Mechanics, Pergamon Press, 1960.
[63] Rand, R.H., Lecture Notes on Nonlinear Vibrations, Cornell University, 2014.
Journal of Applied and Computational Mechanics