IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v216y2024icp168-186.html
   My bibliography  Save this article

A robust computational analysis of residual power series involving general transform to solve fractional differential equations

Author

Listed:
  • Khirsariya, Sagar R.
  • Chauhan, Jignesh P.
  • Rao, Snehal B.

Abstract

In this paper, we provide a new semi-analytical approach, General Residual Power Series Method (GRPSM), to solve fractional differential equations (FDEs). This technique is simple and effective for finding an accurate and approximate solution to linear and nonlinear FDEs. Furthermore, the graphical and numerical results are described in various fractional orders. The solution obtained by GRPSM is compared with Adomian decomposition and Homotopy analysis transform method. We have solved fractional ordered gas dynamics equations and drainage equations using GRPSM, to show the applicability and simplicity of this method.

Suggested Citation

  • Khirsariya, Sagar R. & Chauhan, Jignesh P. & Rao, Snehal B., 2024. "A robust computational analysis of residual power series involving general transform to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 168-186.
    • Handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:168-186
    DOI: 10.1016/j.matcom.2023.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423003890
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.09.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    3. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    4. Khirsariya, Sagar R. & Rao, Snehal B. & Chauhan, Jignesh P., 2023. "A novel hybrid technique to obtain the solution of generalized fractional-order differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 272-290.
    5. Omar Abu Arqub & Zaer Abo-Hammour & Ramzi Al-Badarneh & Shaher Momani, 2013. "A Reliable Analytical Method for Solving Higher-Order Initial Value Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
    6. Jagdev Singh & Devendra Kumar & A. Kılıçman, 2013. "Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dubey, Ved Prakash & Singh, Jagdev & Alshehri, Ahmed M. & Dubey, Sarvesh & Kumar, Devendra, 2022. "Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Samir A. El-Tantawy & Rasool Shah & Albandari W. Alrowaily & Nehad Ali Shah & Jae Dong Chung & Sherif. M. E. Ismaeel, 2023. "A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    3. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Muhammed I. Syam, 2017. "Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method," Complexity, Hindawi, vol. 2017, pages 1-6, August.
    5. Qi, Jianming & Li, Xinwei & Bai, Leiqiang & Sun, Yiqun, 2023. "The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    6. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    7. Korkmaz, Alper, 2017. "Exact solutions of space-time fractional EW and modified EW equations," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 132-138.
    8. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Mohammed Shqair & Ahmad El-Ajou & Mazen Nairat, 2019. "Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    10. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    11. Az-Zo’bi, Emad A. & Yıldırım, Ahmet & AlZoubi, Wael A., 2019. "The residual power series method for the one-dimensional unsteady flow of a van der Waals gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 188-196.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:168-186. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.