[1] G. Y. Zhang, J. Gao, B. Q. Xiao, L. Chen, J. Y. Cao, G. B. Long, H. R. Hu, Fractal study on the permeability of power-law fluid in a rough and damaged tree-like branching network, Phys. Fluids, Vol. 36, 2024.
[2] M. X. Liu, J. Gao, B. Q. Xiao, P. L. Wang, H. Z. Y. Li, S. F. Li, G. B. Long, Y. Xu, Fractal model for effective thermal conductivity of composite materials embedded with a damaged tree-like bifurcation network, Fractals, Vol. 32, 2024.
[3] P. Zhang, J. Y. Ding, J. J. Guo, F. Wang, Fractal analysis of cement-based composite microstructure and its application in evaluation of macroscopic performance of cement-based composites: a review, Fractal Fract, Vol. 8, 2024.
[4] M. Ungarish, Self-similar flow of Newtonian and power-law viscous gravity currents in a confining gap in rectangular and axisymmetric geometries, J. Fluid Mech, Vol. 1007, 2025.
[5] N. Anjum, C. H. He, J. H. He, Two-scale fractal theory for the population dynamics Fractals, Vol. 29, 2021.
[6] N. Anjum, Q. T. Ain, X. X. Li, Two-scale mathematical model for tsunami wave, Gem-Int. J. Geomat, Vol. 12, pp. 1-12, 2021.
[7] Y. R. Zhang, N. Anjum, D. Tian, A. A. Alsolami, Fast and accurate population forecasting with two-scale fractal population dynamics and its application to population economics, Fractals, Vol. 32, 2024.
[8] J. H. He, Y. O. El-Dib, A tutorial introduction to the two-scale fractal calculus and its application to the fractal Zhiber-Shabat oscillator, Fractals, Vol. 29, 2021.
[9] A. Elias-Zuniga, O. Martinez-Romero, D. O. Trejo, L. M. Palacios-Pineda, Fractal equation of motion of a non-Gaussian polymer chain: investigating its dynamic fractal response using an ancient Chinese algorithm, J. Math. Chem, Vol. 60, pp. 461-473, 2022.
[10] H. Y. Song, A thermodynamic model for a packing dynamical system, Thermal Science, Vol. 24, pp. 2331-2335, 2020.
[11] M. Bayat, I. Pakar, M. Bayat, M. Bayat, I. Pakar, M. Bayat, Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review, Lat. Am. J. Solids Struct, Vol. 9, pp. 145-234, 2012.
[12] B. Moussa, M. Youssouf, N. A. Wassiha, P. Youssouf, Homotopy perturbation method to solve Duffing-Van der Pol equation, Adv. Differ. Equ. Control Process, Vol. 31, pp. 299-315, 2024.
[13] G. Q. Feng, Higher-order homotopy perturbation method for the fractal rotational pendulum oscillator, J. Vib. Eng. Technol, Vol. 12, pp. 2829-2834, 2024.
[14] J. H. He, C. H. He, A. A. Alsolami, A good initial guess for approximating nonlinear oscillators by the homotopy perturbation method, Facta Univ. Ser. Mech. Eng, Vol. 21, No. 1, pp. 21-29, 2023.
[15] N. A. M. Alshomrani, W. G. Alharbi, I. M. A. Alanazi, L. S. M. Alyasi, G. N. M. Alrefaei, S. A. Al'Amri, A. H. Q. Alanzi, Homotopy perturbation method for solving a nonlinear system for an epidemic, Adv. Differ. Equ. Control Process, Vol. 31, pp. 347-355, 2024.
[16] N. Anjum, A. Rasheed, J. H. He, A. A. Alsolami, Free vibration of a tapered beam by the Aboodh transformbased variational iteration method, J. Comput. Appl. Mech, Vol. 55, pp. 440-450, 2024.
[17] X. Wang, T. A. Elgohary, Z. Zhang, T. H. Tasif, H. Y. Feng, S. N. Atluri, An adaptive local variational iteration method for orbit propagation in astrodynamics problems, J. Astronaut. Sci, Vol. 70, 2023.
[18] A. A. Rossikhin, V. I. Mileshin, Application of the harmonic balance method to calculate the first booster stage tonal noise, Math. Model. Comput. Simul, Vol. 16, pp. 63-75, 2024.
[19] Q. S. Wang, Z. P. Yan, H. H. Da, An efficient multiple harmonic balance method for computing quasi-periodic responses of nonlinear systems, J. Sound Vib, Vol. 554, 2023.
[20] J. Li, Y. F. Xin, T. T. Murmy, Exploring comfort and vibration dampening in fashion design in fabrics with innovative use of nanoparticle additives, Adv. Nano Res, Vol. 17, pp. 465-471, 2024.
[21] Y. Zhang, Q. H. Guo, X. H. Wan, L. Y. Zheng, Subwavelength topological edge states in a mechanical analogy of nanoparticle chain, New J. Phys, Vol. 27, 2025.
[22] D. Arifin, S. Mcwilliam, Negating self-induced parametric excitation in capacitive ring-based MEMS Coriolis vibrating gyroscopes, J. Sound Vib, Vol. 607, 2025.
[23] C. H. He, A variational principle for a fractal nano/microelectromechanical (N/MEMS) system, Int. J. Numer. Methods Heat Fluid Flow, Vol. 33, pp. 351-359, 2023.
[24] J. H. He, C. H. He, A. A. Alsolami, Periodic solution of a micro-electromechanical system, Facta Univ. Ser. Mech. Eng, Vol. 22, pp. 187-198, 2024.
[25] J. Song, C. Xia, G. S. Shan, Z. Q. Wang, T. Ono, G. G. Cheng, D. F. Wang, Temperature sensing and energy harvesting with a MEMS parametric coupling device under low frequency vibrations, J. Sound Vib, Vol. 585, 2024.
[26] Y. O. El-Dib, Stability analysis of a time-delayed Van der Pol-Helmholtz-Duffing oscillator in fractal space with a non-perturbative approach, Commun. Theor. Phys, Vol. 76, 2024.
[27] Y. O. El-Dib, N. S. Elgazery, Y. M. Khattab, H. A. Alyousef, An innovative technique to solve a fractal damping Duffing-jerk oscillator, Commun. Theor. Phys, Vol. 75, 2023.
[28] G. M. Ismail, G.M. Moatimid, M. I. Yamani, Periodic solutions of strongly nonlinear oscillators using He’s frequency formulation, Eur. J. Pure Appl. Math, Vol. 17, pp. 2155-2172, 2024.
[29] G. Hashemi, A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He’s frequency-amplitude formulation, Comput. Methods Differ. Equ, Vol. 11, pp. 464-477, 2023.
[30] J. H. He, The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators, J. Low Freq. Noise Vib. Act. Control, Vol. 38, pp. 1252-1260, 2019.
[31] M. A. Kawser, M. A. Alim, N. Sharif, Analyzing nonlinear oscillations with He’s frequency-amplitude method and numerical comparison in jet engine vibration system, Heliyon, Vol. 10, 2024.
[32] K. Tsaltas, An improved one-step amplitude-frequency relation for nonlinear oscillators, Results Phys, Vol. 54, 2023.
[33] J. H. He, Frequency-amplitude relationship in nonlinear oscillators with irrational nonlinearities, Spectr. Mech. Eng. Oper. Res, Vol. 2, pp. 121-129, 2025.
[34] J. H. He, The simplest approach to nonlinear oscillators, Results Phys, Vol. 15, 2019.
[35] Y. O. El-Dib, N. S. Elgazery, A novel pattern in a class of fractal models with the non-perturbative approach, Chaos Solitons Fractals, Vol. 164, 2022.
[36] Y. O. El-Dib, N. S. Elgazery, An efficient approach to converting the damping fractal models to the traditional system, Commun. Nonlinear Sci. Numer. Simul, Vol. 118, 2023.
[37] Y. O. El-Dib, A dynamic study of a bead sliding on a wire in fractal space with the non-perturbative technique, Arch. Appl. Mech, Vol. 94, pp. 571-588, 2024.
[38] G. M. Moatimid, Sliding bead on a smooth vertical rotated parabola: stability configuration, Kuwait J. Sci, Vol. 47, pp. 6-21, 2020.