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Relevant bibliographies by topics / Fractional Homotopy Perturbation Method

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Academic literature on the topic 'Fractional Homotopy Perturbation Method'

Author: Grafiati

Published: 7 June 2025

Last updated: 16 July 2025

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Journal articles on the topic "Fractional Homotopy Perturbation Method"

1

Dhumal, Meenakshi, and Bhausaheb Sontakke. "Solving Time-Fractional Fitzhugh–Nagumo Equation using Homotopy Perturbation Method." Indian Journal Of Science And Technology 17, no. 13 (2024): 1272–82. http://dx.doi.org/10.17485/ijst/v17i13.3009.

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Objectives: This study aims to explore solutions to the time-fractional Fitzhugh-Nagumo equation, a nonlinear reaction-diffusion equation. Method: We utilize the Homotopy Perturbation Method (HPM) as a proficient analytical approach for addressing the time-fractional Fitzhugh-Nagumo equation. The HPM offers a structured method for deriving approximate solutions in the shape of convergent series, enabling accurate solutions even for intricate nonlinear fractional equations. Finding: The series solution obtained is validated by comparing it with numerical methods, showcasing its precision and effectiveness. Additionally, we assessed the error across various time and space values. Our analysis and computations reveal that the Homotopy Perturbation Method (HPM) stands out for providing precise approximations while maintaining computational efficiency. It's clear that this method presents a robust alternative to conventional numerical techniques, particularly in situations where analytical solutions are difficult to obtain. Novelty: The application of the Homotopy Perturbation Method to the Time-fractional Fitzhugh-Nagumo Equation has been effectively explored, with specific examples showing a strong agreement between the exact solution and the obtained solution. Keywords: Time-Fractional Fitzhugh–Nagumo Equation, Homotopy Perturbation Method, Riemann-Liouville fractional integral, Caputo fractional derivative, Fractional Homotopy Perturbation Method

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Singh, Prince, and Dinkar Sharma. "Comparative study of homotopy perturbation transformation with homotopy perturbation Elzaki transform method for solving nonlinear fractional PDE." Nonlinear Engineering 9, no. 1 (2019): 60–71. http://dx.doi.org/10.1515/nleng-2018-0136.

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AbstractWe apply homotopy perturbation transformation method (combination of homotopy perturbation method and Laplace transformation) and homotopy perturbation Elzaki transformation method on nonlinear fractional partial differential equation (fpde) to obtain a series solution of the equation. In this case, the fractional derivative is described in Caputo sense. To avow the adequacy and authenticity of the technique, we have applied both the techniques to Fractional Fisher’s equation, time-fractional Fornberg-Whitham equation and time fractional Inviscid Burgers’ equation. Finally, we compare the results obtained from homotopy perturbation transformation technique with homotopy perturbation Elzaki transformation.

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Meenakshi, Dhumal, and Sontakke Bhausaheb. "Solving Time-Fractional Fitzhugh–Nagumo Equation using Homotopy Perturbation Method." Indian Journal of Science and Technology 17, no. 13 (2024): 1272–82. https://doi.org/10.17485/IJST/v17i13.3009.

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Abstract <strong>Objectives:</strong> This study aims to explore solutions to the time-fractional Fitzhugh-Nagumo equation, a nonlinear reaction-diffusion equation. <strong>Method:</strong> We utilize the Homotopy Perturbation Method (HPM) as a proficient analytical approach for addressing the time-fractional Fitzhugh-Nagumo equation. The HPM offers a structured method for deriving approximate solutions in the shape of convergent series, enabling accurate solutions even for intricate nonlinear fractional equations. <strong>Finding:</strong> The series solution obtained is validated by comparing it with numerical methods, showcasing its precision and effectiveness. Additionally, we assessed the error across various time and space values. Our analysis and computations reveal that the Homotopy Perturbation Method (HPM) stands out for providing precise approximations while maintaining computational efficiency. It's clear that this method presents a robust alternative to conventional numerical techniques, particularly in situations where analytical solutions are difficult to obtain. <strong>Novelty:</strong> The application of the Homotopy Perturbation Method to the Time-fractional Fitzhugh-Nagumo Equation has been effectively explored, with specific examples showing a strong agreement between the exact solution and the obtained solution. <strong>Keywords:</strong> Time-Fractional Fitzhugh–Nagumo Equation, Homotopy Perturbation Method, Riemann-Liouville fractional integral, Caputo fractional derivative, Fractional Homotopy Perturbation Method

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Dhumal, Meenakshi, Bhausaheb Sontakke, and Jagdish Sonawane. "Solving Time-Space Fractional Boussinesq Equation Using Homotopy Perturbation Method." European Journal of Mathematics and Statistics 5, no. 6 (2024): 1–6. http://dx.doi.org/10.24018/ejmath.2024.5.6.377.

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This paper aims to implement the homotopy perturbation technique to solve the time-space fractional Boussinesq equation, a significant model in the analysis of nonlinear wave propagation. Through the application of the homotopy perturbation technique, we derive analytical expressions for the solutions of the time-space fractional Boussinesq equation and validate these solutions through comparisons with numerical methods. Obtained results demonstrate the efficiency and accuracy of the homotopy perturbation method in solving the time-space fractional Boussinesq equation.

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Malo, Diyar Hashim, Rogash Younis Masiha, Muhammad Amin Sadiq Murad, and Sadeq Taha Abdulazeez. "A New Computational Method Based on Integral Transform for Solving Linear and Nonlinear Fractional Systems." Jurnal Matematika MANTIK 7, no. 1 (2021): 9–19. http://dx.doi.org/10.15642/mantik.2021.7.1.9-19.

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In this article, the Elzaki homotopy perturbation method is applied to solve fractional stiff systems. The Elzaki homotopy perturbation method (EHPM) is a combination of a modified Laplace integral transform called the Elzaki transform and the homotopy perturbation method. The proposed method is applied for some examples of linear and nonlinear fractional stiff systems. The results obtained by the current method were compared with the results obtained by the kernel Hilbert space KHSM method. The obtained result reveals that the Elzaki homotopy perturbation method is an effective and accurate technique to solve the systems of differential equations of fractional order.

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Alqhtani, Manal, Khaled M. Saad, Rasool Shah, Thongchai Botmar, and Waleed M. Hamanah. "Evaluation of fractional-order equal width equations with the exponential-decay kernel." AIMS Mathematics 7, no. 9 (2022): 17236–51. http://dx.doi.org/10.3934/math.2022949.

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<abstract><p>In this article we consider the homotopy perturbation transform method to investigate the fractional-order equal-width equations. The homotopy perturbation transform method is a mixture of the homotopy perturbation method and the Yang transform. The fractional-order derivative are defined in the sense of Caputo-Fabrizio operator. Several fractions of solutions are calculated which define some valuable evolution of the given problems. The homotopy perturbation transform method results are compared with actual results and good agreement is found. The suggested method can be used to investigate the fractional perspective analysis of problems in a variety of applied sciences.</p></abstract>

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Saadeh, Rania, Ahmad Qazza, and Abdelilah Kamal Sedeeg. "A Generalized Hybrid Method for Handling Fractional Caputo Partial Differential Equations via Homotopy Perturbed Analysis." WSEAS TRANSACTIONS ON MATHEMATICS 22 (December 31, 2023): 988–1000. http://dx.doi.org/10.37394/23206.2023.22.108.

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This article describes a novel hybrid technique known as the Sawi transform homotopy perturbation method for solving Caputo fractional partial differential equations. Combining the Sawi transform and the homotopy perturbation method, this innovative technique approximates series solutions for fractional partial differential equations. The Sawi transform is a recently developed integral transform that may successfully manage recurrence relations and integro-differential equations. Using a homotopy parameter, the homotopy perturbation method is a potent semi-analytical tool for constructing approximate solutions to nonlinear problems. The suggested method offers various advantages over existing methods, including high precision, rapid convergence, minimal computing expense, and broad applicability. The new method is used to solve the convection–reaction–diffusion problem using fractional Caputo derivatives.

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Yasmin, Humaira. "Application of Aboodh Homotopy Perturbation Transform Method for Fractional-Order Convection–Reaction–Diffusion Equation within Caputo and Atangana–Baleanu Operators." Symmetry 15, no. 2 (2023): 453. http://dx.doi.org/10.3390/sym15020453.

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This article is an analysis of fractional nonlinear convection–reaction–diffusion equations involving the fractional Atangana–Baleanu and Caputo derivatives. An efficient Aboodh homotopy perturbation transform method, which combines the homotopy perturbation method with the Aboodh transformation, is applied to investigate this fractional-order proposed model, analytically. A modified technique known as the Aboodh homotopy perturbation transform method is formulated to approximate these derivatives. The analytical simulation is investigated graphically as well as in tabular form.

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Al-Khaled, Kamel, and M. K. Al-Safeen. "Homotopy Perturbation Method For Fractional Shallow Water Equations." Sultan Qaboos University Journal for Science [SQUJS] 19, no. 1 (2014): 74. http://dx.doi.org/10.24200/squjs.vol19iss1pp74-86.

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In this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis method, to solve certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. The results obtained reveal that these methods are both very effective and simple for finding approximate solutions. Some numerical examples and plots are presented to illustrate the efficiency and reliability of these methods.

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Yavuz, Mehmet, and Necati Ozdemir. "Numerical inverse Laplace homotopy technique for fractional heat equations." Thermal Science 22, Suppl. 1 (2018): 185–94. http://dx.doi.org/10.2298/tsci170804285y.

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In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He?s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approximate solutions to the fractional PDE.

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Dissertations / Theses on the topic "Fractional Homotopy Perturbation Method"

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Thapa, Chandra B. "On the Homotopy Perturbation Method for Nonlinear Oscillators." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1570793395580841.

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Ncube, Mahluli Naisbitt. "The natural transform decomposition method for solving fractional differential equations." Diss., 2018. http://hdl.handle.net/10500/25348.

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In this dissertation, we use the Natural transform decomposition method to obtain approximate analytical solution of fractional differential equations. This technique is a combination of decomposition methods and natural transform method. We use the Adomian decomposition, the homotopy perturbation and the Daftardar-Jafari methods as our decomposition methods. The fractional derivatives are considered in the Caputo and Caputo- Fabrizio sense.<br>Mathematical Sciences<br>M. Sc. (Applied Mathematics)

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Sahoo, Malika. "Some Applications of Homotopy Perturbation Method." Thesis, 2015. http://ethesis.nitrkl.ac.in/7072/1/Some_Sahoo_2015.pdf.

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In this thesis paper, I review the basic idea of Homotopy perturbation method (HPM), Modified Homotopy perturbation method (MHPM) and Homotopy perturbation transform method (HPTM). Then apply these on some higher order non-linear problems.Further, I tried to compare the results obtained from Modified homotopy perturbation method with HPM using the Sine-Gordon and fractional Klein-Gordon equation respectively. Homotopy perturbation transform method is the coupling of homotopy perturbation and Laplace transform method. Lastly, I applied the homotopy perturbation and homotopy perturbation transform method for solving linear and non-linear Schrödinger equations

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Liu, Kai-yuan, and 劉凱元. "Homotopy Perturbation Method for Van Der Pol Equation." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/63672681267689054510.

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碩士<br>國立政治大學<br>應用數學研究所<br>93<br>In this thesis, we study the limit cycle of van der Pol equation for parameter ε>0. We give some approximate results to the limit cycle by using the modified homotopy perturbation technique. In constract to the traditional perturbation methods, this homotopy method does not require a small parameter in the equation. Besides, we also devise a new algorithm to find the approximate amplitude and frequency of the limit cycle.

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Oguntala, George A., G. Sobamowo, Y. Ahmed, and Raed A. Abd-Alhameed. "Application of approximate analytical technique using the homotopy perturbation method to study the inclination effect on the thermal behavior of porous fin heat sink." 2018. http://hdl.handle.net/10454/16637.

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Yes<br>This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length–thickness aspect ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge–Kutta.<br>Supported in part by the Tertiary Education Trust Fund of Federal Government of Nigeria, and the European Union’s Horizon 2020 research and innovation programme under grant agreement H2020-MSCA-ITN-2016SECRET-722424.

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Books on the topic "Fractional Homotopy Perturbation Method"

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Liao, Shijun. Beyond perturbation: Introduction to homotopy analysis method. Chapman & Hall/CRC Press, 2004.

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Beyond perturbation: Introduction to the homotopy analysis method. Chapman & Hall/CRC Press, 2004.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method (Modern Mathematics and Mechanics). Chapman & Hall/CRC, 2003.

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Soori, Mohsen, and S. Salman Nourazar. On the Exact Solution of Nonlinear Differential Equations Using Variational Iteration Method and Homotopy Perturbation Method. GRIN Verlag GmbH, 2019.

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Book chapters on the topic "Fractional Homotopy Perturbation Method"

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Dubey, Shweta, and S. Chakraverty. "Homotopy Perturbation Method for Solving Fuzzy Fractional Heat-Conduction Equation." In Advances in Fuzzy Integral and Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73711-5_6.

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Kashyap, Manju, Surbhi Gupta, H. D. Arora, and Amit Kumar Verma. "Numerical Analysis of Nanoparticle Diffusion: Solving Time-Fractional Klein–Gordon Equations with the Laplace Homotopy Perturbation Method." In Studies in Systems, Decision and Control. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-84955-8_10.

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Marinca, Vasile, and Nicolae Herisanu. "The Optimal Homotopy Perturbation Method." In Nonlinear Dynamical Systems in Engineering. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22735-6_7.

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Odibat, Zaid, and Cyrille Bertelle. "Application of Homotopy Perturbation Method for Ecosystems Modelling." In Understanding Complex Systems. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-88073-8_5.

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Zephania, C. F. Sagar, and Tapas Sil. "An improved homotopy perturbation method to study damped oscillators." In Aerospace and Associated Technology. Routledge, 2022. http://dx.doi.org/10.1201/9781003324539-70.

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Zulkarnain, F. S., Z. K. Eshkuvatov, N. M. A. Nik Long, and F. Ismail. "Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation." In Recent Advances in Mathematical Sciences. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0519-0_4.

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Jani, Haresh P., and Twinkle R. Singh. "Aboodh Transform Homotopy Perturbation Method for Solving Newell–Whitehead–Segel Equation." In Computational and Analytic Methods in Biological Sciences. River Publishers, 2023. http://dx.doi.org/10.1201/9781003393238-9.

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Yazid, Nazatulsyima Mohd, Kim Gaik Tay, Yaan Yee Choy, and Azila Md Sudin. "Solving Nonlinear Schrodinger Equation with Variable Coefficient Using Homotopy Perturbation Method." In Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015). Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2772-7_26.

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Fatima, Nahid, and Monika Dhariwal. "Solutions of Differential Equations for Prediction of COVID-19 Cases by Homotopy Perturbation Method." In Intelligent Computing Applications for COVID-19. CRC Press, 2021. http://dx.doi.org/10.1201/9781003141105-3.

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Georgieva, Atanaska, and Artan Alidema. "Convergence of Homotopy Perturbation Method for Solving of Two-Dimensional Fuzzy Volterra Functional Integral Equations." In Advanced Computing in Industrial Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97277-0_11.

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Conference papers on the topic "Fractional Homotopy Perturbation Method"

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Liu, Yapeng, and Xiaoshan Zhao. "Application of Homotopy Perturbation Method in Solving Fractional Cahn-Allen Equation." In 2024 3rd International Conference on Cloud Computing, Big Data Application and Software Engineering (CBASE). IEEE, 2024. https://doi.org/10.1109/cbase64041.2024.10824608.

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Jassim, Hassan Kamil, Ali Thamir Salman, Hijaz Ahmad, Nabeel Jawad Hassan, and Ayed E. Hashoosh. "Solving nonlinear fractional PDEs by Elzaki homotopy perturbation method." In 2ND INTERNATIONAL CONFERENCE OF MATHEMATICS, APPLIED SCIENCES, INFORMATION AND COMMUNICATION TECHNOLOGY. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0161551.

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Madhavi, B., G. Suresh Kumar, and T. Srinivasa Rao. "Homotopy perturbation method for solution of q-fractional differential equations." In 2ND INTERNATIONAL CONFERENCE ON ADVANCED INFORMATION SCIENTIFIC DEVELOPMENT (ICAISD) 2021: Innovating Scientific Learning for Deep Communication. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0143137.

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Raba, Bana Ali, and Fadime Dal. "Homotopy Perturbation Method Applied to Fractional-order Nonlinear Partial Differential Equations." In 8th International Students Science Congress. ULUSLARARASI ÖĞRENCİ DERNEKLERİ FEDERASYONU (UDEF), 2024. https://doi.org/10.52460/issc.2024.034.

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In this paper, we propose a numerical method for solving nonlinear fractional partial differential equations with fractional time derivatives. The fractional derivative is described in the Caputo sense. This method is based on the homotopy perturbation method. The approximate solutions obtained by our proposed method are in excellent agreement with the exact solutions. It is worthwhile to note that our method is applicable to a variety of fractional partial differential equations occurring in fluid mechanics, signal processing, system identification, control, and robotics.

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Sahib, Ali Adnan Abdul, and Fadhel S. Fadhel. "Solution of fractional order random integro-differential equations using homotopy perturbation method." In THE SECOND INTERNATIONAL SCIENTIFIC CONFERENCE (SISC2021): College of Science, Al-Nahrain University. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0118906.

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Mohammed, Sahar A., Fadhel S. Fadhel, and Kasim A. Hussain. "Approximate solution of fractional order random ordinary differential equations using homotopy perturbation method." In FIFTH INTERNATIONAL CONFERENCE ON APPLIED SCIENCES: ICAS2023. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0209932.

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Kumaresan, N., and Kuru Ratnavelu. "An approximate analytical solution of fractional 2D Navier-Stokes equation using homotopy-perturbation method." In THE 22ND NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM22): Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4932437.

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Ibrahim, Anfal Khalil, and Basim Albuohimad. "On a hybrid g-transform homotopy perturbation method for solution of fractional differential equations." In 4TH INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0182169.

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Singh, Brajesh Kumar, та Anil Kumar. "New approximations of fractional Klein-Fock Gordon equations via homotopy perturbation 𝕁-transform method". У 2nd INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCES-MODELLING, COMPUTING AND SOFT COMPUTING (CSMCS 2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0154115.

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Albuohimad, Basim K. "Analytical technique of the fractional Navier-Stokes model by Elzaki transform and homotopy perturbation method." In THE 7TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY (ICAST 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5123118.

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