IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics0960077922001941.html
   My bibliography  Save this article

Adaptation on power series method with conformable operator for solving fractional order systems of nonlinear partial differential equations

Author

Listed:
  • Liaqat, Muhammad Imran
  • Khan, Adnan
  • Akgül, Ali

Abstract

The aim of this research work is to modify the power series solution method to fractional order in the sense of conformable derivative to solve a coupled system of nonlinear fractional partial differential equations. We called it the conformable fractional power series method. To evaluate its efficiency and consistency, absolute errors of three problems are considered numerically. Consequences established that our recommended method is unpretentious, accurate, valid, and capable. When solving the nonlinear complications, it has a powerful superiority over the homotopy analysis and Adomian decomposition methods. Additional as in the residual power series method through generating the coefficients for a series, it is compulsory to calculate the fractional derivatives on every occasion, whereas this method only needs the idea of equating coefficients. The convergence and error analyses of the series solutions are also presented.

Suggested Citation

  • Liaqat, Muhammad Imran & Khan, Adnan & Akgül, Ali, 2022. "Adaptation on power series method with conformable operator for solving fractional order systems of nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001941
    DOI: 10.1016/j.chaos.2022.111984
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922001941
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111984?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. E. López-Sandoval & A. Mello & J. J. Godina-Nava & A. R. Samana, 2015. "Power Series Solution for Solving Nonlinear Burgers-Type Equations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-9, October.
    2. Adnan Khan & Muhammad Imran Liaqat & Muhammad Younis & Ashraful Alam & Fairouz Tchier, 2021. "Approximate and Exact Solutions to Fractional Order Cauchy Reaction-Diffusion Equations by New Combine Techniques," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, December.
    3. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Rasool Shah & Hassan Khan & Poom Kumam & Muhammad Arif & Dumitru Baleanu, 2019. "Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay," Mathematics, MDPI, vol. 7(6), pages 1-14, June.
    5. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    6. Bashir Ahmad & Jorge Losada & Juan J. Nieto, 2015. "On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, June.
    7. Mohammed Al-Refai & Mohamed Ali Hajji & Muhammad I. Syam, 2014. "An Efficient Series Solution for Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    8. Haidong Qu & Zihang She & Xuan Liu, 2020. "Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations," Complexity, Hindawi, vol. 2020, pages 1-13, July.
    9. Qinwu Xu & Zhoushun Zheng, 2019. "Spectral Collocation Method for Fractional Differential/Integral Equations with Generalized Fractional Operator," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-14, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    2. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    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. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2022. "Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method," Mathematics, MDPI, vol. 10(12), pages 1-16, June.
    3. Laila F. Seddek & Essam R. El-Zahar & Jae Dong Chung & Nehad Ali Shah, 2023. "A Novel Approach to Solving Fractional-Order Kolmogorov and Rosenau–Hyman Models through the q-Homotopy Analysis Transform Method," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    4. Ndenda, J.P. & Njagarah, J.B.H. & Shaw, S., 2021. "Role of immunotherapy in tumor-immune interaction: Perspectives from fractional-order modelling and sensitivity analysis," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    5. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
    6. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2021. "Adaptation of Residual-Error Series Algorithm to Handle Fractional System of Partial Differential Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    7. Meshari Alesemi & Naveed Iqbal & Thongchai Botmart, 2022. "Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    8. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Martynyuk, Anatoliy A. & Stamov, Gani Tr. & Stamova, Ivanka M., 2020. "Fractional-like Hukuhara derivatives in the theory of set-valued differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    10. Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung, 2022. "An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform," Mathematics, MDPI, vol. 10(5), pages 1-16, March.

    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:chsofr:v:157:y:2022:i:c:s0960077922001941. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.