Laplace Homotopy Perturbation Method (Lhpm) For Solving Systems Of N-Dimensional Non-Linear Partial Differential Equation by Kabir Oluwatobi Idowu, Toluwanimi Grace Akinwande, Ibrahim Fayemi, Umar Muhammad Adam, Adedapo Chris Loyinmi

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A simplified homotopy perturbation method for solving nonlinear ill-posed operator equations in Hilbert spaces by Sharad Kumar Dixit

“… One popular regularization technique for handling both linear and nonlinear ill-posed problems is homotopy perturbation. …”
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Analytical simulation of the nonlinear Caputo fractional equations by Ali Ahadi, Seyed Mostafa Mousavi, Amir Mohammad Alinia, Hossein Khademi

“…This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). …”
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He-Laplace Method for Linear and Nonlinear Partial Differential Equations by Hradyesh Kumar Mishra, Atulya K. Nagar

“…A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. …”
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On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy by Dilveen M. Ahmed, Bewar A. Mahmood, Ahmad Alalyani

“…By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. …”
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Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations by Atia Nazneen, Nasir Ali, Syed M. Hussain, Hijaz Ahmad, Rashid Nawaz, Laiq Zada, Rida Irfan, Kamel Guedri, Abdulrazak H. Almaliki, Mustafa Bayram

“…In comparison with other established techniques, such as the Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), and Fractional Homotopy Analysis Transform Method (FHATM). …”
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Efficient Approach for Solving (2+1) D- Differential Equations by Luma N. M. Tawfiq, Noor A. Hussein

“…The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. …”
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Advancing heat transport in radiated Carreau–Yasuda non-Newtonian fluids under nonlinear stretching conditions and variable heat flux: A similarity solution approach by Mounirah Areshi

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A New Strategy for the Approximate Solution of Hyperbolic Telegraph Equations in Nonlinear Vibration System by Jiao Zeng, Asma Idrees, Mohammed S. Abdo

“…We introduce a Laplace-Carson transform coupled with the homotopy perturbation method which is called the Laplace-Carson homotopy perturbation method (Lc-HPM). …”
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A numerical algorithm based on Jacobi polynomials for FIDEs with error estimation by K. Sadri, D. Amilo, E. Hincal

“…Notably, our approach is simpler and more cost-effective compared to established methods such as Adomian decomposition, Homotopy perturbation, Sinc-collocation, and Legendre wavelet techniques. …”
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Characteristic analysis of a new high-static-low-dynamic stiffness vibration isolator based on the buckling circular plate by Zhirong Yang, Yan Wang, Ziming Huang, Zhushi Rao

“…The nonlinear mathematical model of high-static-low-dynamic stiffness vibration isolator considering load imperfection is developed and its force transmissibility is analyzed with the harmonic balance method and homotopy perturbation method. The influence rule of the system parameters on it is analyzed and the corresponding results show that the force transmissibility will exhibit complicated characteristics, depending on the load imperfection, damper, and excitation force.…”
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Nonlinear Vibration of Multi-Walled Carbon Nanotubes with Initial Curvature Resting on Elastic Foundations in a Nonlinear Thermo-Magnetic Environment by Gbeminiyi Musibau SOBAMOWO, James A. AKANMU, Olurotimi A. ADELEYE, Samuel AKINGBADE, Ahmed Amao YINUSA

“…The derived systems of nonlinear vibration models are solved with the aid of the Galerkin decomposition and the homotopy perturbation method. Effects of temperature, magnetic field, multi-layer, and other thermomechanical parameters on the dynamic responses of the slightly curved multi-walled carbon nanotubes are investigated and discussed. …”
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