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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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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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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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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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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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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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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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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