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### Homotopy Perturbation Method for Solving Generalized Riccati Differential Equation

Mohammed S. Mechee, Ghassan A. Al-Juaifri
2019 Al-Nahrain Journal of Science
Also, we have tested the modified homotopy perturbation method on the solving of different implementations which are show the efficiency and accuracy of the proposed method.  ...  The homotopy perturbation method, has been modified for solving generalized linear and nonlinear Riccati differential equation, which is a second-order ordinary differential equation.  ...  The authors would like to thank university of Kufa for supporting this research project  ...

### Homotopy perturbation solution and periodicity analysis of nonlinear vibration of thin rectangular functionally graded plates

2014 Acta Mechanica Solida Sinica
The homotopy perturbation solution of generated Duffing's equation is also obtained and compared with numerical solutions.  ...  By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing's equation.  ...  As depicted in this figure, the homotopy perturbation method agrees very well with numerical solution. IV. PERIODICITY ANALYSIS Equation (34) belongs to the class of Duffing equations  .  ...

### He's Homotopy Perturbation Method and Fractional Complex Transform for Analysis Time Fractional Fornberg-Whitham Equation

Yanni Zhang, Jing Pang
2021 Sound & vibration
To transform the fractional model into its equivalent differential equation, the fractional complex transform is used and He's homotopy perturbation method is implemented to get the approximate analytical  ...  The graphs are plotted to analysis the fractional-order mathematical modeling.  ...  The homotopy perturbation method (HPM)    is widely applied to various science and engineering problems. This method was first proposed by He  .  ...

### COMPUTATIONAL SOLUTION OF TEMPERATURE DISTRIBUTION IN A THIN ROD OVER A GIVEN INTERVAL I={x├|0<x<1┤}

Falade Kazeen Iyanda, Ismail Baoku, Gwanda Yusuf Ibrahim
2021 FUDMA Journal of Sciences
In this paper, two analytical–numerical algorithms are formulated based on homotopy perturbation method and new iterative method to obtain numerical solution for temperature distribution in a thin rod  ...  Thus, the algorithms are established as good numerical tools to solve several problems in applied mathematics and other related field of sciences  ...  Furthermore, Xiao et al. (2015) proposed a local fractional homotopy perturbation method which was an extended form of the classical homotopy perturbation method.  ...

### THE ENHANCED HOMOTOPY PERTURBATION METHOD FOR AXIAL VIBRATION OF STRINGS

Ji-Huan He, Yusry O. El-Dib
2021 Facta Universitatis. Series: Mechanical Engineering
The classical homotopy perturbation method (HPM) fails to analyze this equation, and a modification with an exponential decay parameter is suggested.  ...  The modified homotopy perturbation method yields a more effective result for the nonlinear oscillators and helps to overcome the shortcoming of the classical approach.  ...  El-Dib  introduced the multiple-scale homotopy perturbation method (He's multiple-scale method) as an outer perturbation of the nonlinear KG equation.  ...

### Homotopy Perturbation Method for the Fractal Toda Oscillator

Ji-Huan He, Yusry O. El-Dib, Amal A. Mady
2021 Fractal and Fractional
The homotopy perturbation method is used to solve the fractal Toda oscillator, and the analytical solution is examined using the numerical solution which shows excellent agreement.  ...  In this paper, first, the fractal variational theory is used to show the basic property of the fractal oscillator, and a new form of the Toda oscillator is obtained free of the exponential nonlinear term  ...  The homotopy perturbation method was adopted to solve the nonlinear third-order differential equation, and the results are good enough for practical applications.  ...

### Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method

R. Yulita Molliq, M. S. M. Noorani
2012 International Journal of Differential Equations
We implement relatively new analytical techniques, the variational iteration method and the homotopy perturbation method, for solving this equation.  ...  The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for fractional Rosenau-Hynam equations.  ...  For the application of HPM, this method used for solving fractional vibration equation 26 and partial differential equations of fractional order in finite domains 27 .  ...

### Application of Homotopy Perturbation Method for SIR Model with Vital Dynamics and Constant Population

Mohammed S. Mechee, Ghassan A. Al-Juaifri
2018 American Journal of Applied Sciences
The Homotopy Perturbation Method (HPM) and Runge-Kutta method (RK) have been used for solving the SIR model with vital dynamics and constant population. The convergence of HPM has been studied.  ...  Also, we have tested the HPM on solving different implementations which are show the efficiency and accuracy of the method.  ...  Acknowledgement The authors would like to thank university of Kufa for supporting this research project.  ...

### Stability Analysis of a Damped Nonlinear Wave Equation

Yusry O. El-Dib, Galal M. Moatimid, Nasser S. Elgazery
2020 Journal of Applied and Computational Mechanics
Furthermore, the initial conditions are included throughout the multiple scale method to achieve a special solution of the governing equation of motion.  ...  The Riemann-Liouville fractional calculus is utilized to obtain an analytic approximate solution. The Homotopy technique is absorbed in the multiple time-spatial scales.  ...  Acknowledgments The authors are thankful to all reviewers for their valuable, encouraging comments and constructive suggestions to improve the original version.  ...

### Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System

Xiang Hong, Jun Wang, Li-xin Lu
2013 Mathematical Problems in Engineering
The homotopy perturbation method (HPM) with an auxiliary term was applied to obtain approximate analytical solutions of polymer cushioning packaging system.  ...  The second-order solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm.  ...  Besides, in order to avoid some restrictions of perturbation method, some other methods are developed, including the variational iteration method (VIM)  , the homotopy analysis method (HAM)  ,  ...

### Analytical and Approximate Solution for Solving the Vibration String Equation with a Fractional Derivative

Temirkhan S. Aleroev, Asmaa M. Elsayed
2020 Mathematics
This paper is proposed for solving a partial differential equation of second order with a fractional derivative with respect to time (the vibration string equation), where the fractional derivative order  ...  We propose a numerical solution that is based on the Laplace transform method with the homotopy perturbation method.  ...  Acknowledgments: The authors express their gratitude to the Editorial Board and reviewers for their attention to our work and comments that allowed us to improve the quality of our work.  ...

### An efficient technique for fractional modified Boussinesq and approximate long wave equations [article]

P. Veeresha, D. G. Prakasha, M. A. Qurashi, D. Baleanu
2019 arXiv   pre-print
In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely q-homotopy analysis transform method  ...  We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis has been discussed to verify the accuracy.  ...  In connection with this, Liao proposed a technique called homotopy analysis method (HAM) and which is based on construction of a homotopy which continuously deforms an initial guess approximation to the  ...

### NONLINEAR FREE VIBRATION OF SIMPLY SUPPORTED BEAMS CONSIDERING THE EFFECTS OF SHEAR DEFORMATION AND ROTARY INERTIA, A HOMOTOPY PERTURBATION APPROACH

2011 International Journal of Modern Physics B
The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear  ...  Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation.  ...  His new method takes full advantages of the traditional perturbation methods and homotopy techniques.  ...

### Analytical Analysis of Fractional-Order Physical Models via a Caputo-Fabrizio Operator

Fatemah Mofarreh, A. M. Zidan, Muhammad Naeem, Rasool Shah, Roman Ullah, Kamsing Nonlaopon, Feliz Minhos
2021 Journal of Function Spaces
The Laplace transform and the Adomian decomposition method are implemented to obtain the result of the given models.  ...  This paper investigates a modified analytical method called the Adomian decomposition transform method for solving fractional-order heat equations with the help of the Caputo-Fabrizio operator.  ...  coupling of the homotopy perturbation method and Laplace  D. Rostamy and K.  ...

### A comparison study of the mathematical model of HIV infection of CD4+T cells using homotopy perturbation and variational iteration methods

Ghassan A. AL-Juaifri, Zahrah Ismael Salman, Mohammed S. Mechee
2018 Applied Mathematical Sciences
Homotopy perturbation and variational iteration methods have been studied to introduce an approximated solutions of the systems of ordinary differential equations.  ...  The main objective of this paper is to apply homotopy perturbation and variational iteration approaches to evaluate the uninfected CD + 4 T cells in the body.  ...  The authors would like to thank university of Kufa for supporting this research project.  ...
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