IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p615-d751316.html
   My bibliography  Save this article

Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel

Author

Listed:
  • Meshari Alesemi

    (Department of Mathematics, College of Science, University of Bisha, P.O. Box 511, Bisha 61922, Saudi Arabia)

  • Naveed Iqbal

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Thongchai Botmart

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

This article presents a homotopy perturbation transform method and a variational iterative transform method for analyzing the fractional-order non-linear system of the unsteady flow of a polytropic gas. In this method, the Yang transform is combined with the homotopy perturbation transformation method and the variational iterative transformation method in the sense of Caputo–Fabrizio. A numerical simulation was carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches are effective and efficient in investigating complicated non-linear models. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a very useful way, and this provides us with a simple process to adjust and control the convergence regions of the series solution.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:615-:d:751316
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/615/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/615/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Ahmet Ocak Akdemir & Saad Ihsan Butt & Muhammad Nadeem & Maria Alessandra Ragusa, 2021. "New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    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. Mohammed Kbiri Alaoui & Kamsing Nonlaopon & Ahmed M. Zidan & Adnan Khan & Rasool Shah, 2022. "Analytical Investigation of Fractional-Order Cahn–Hilliard and Gardner Equations Using Two Novel Techniques," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

    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. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    2. Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
    3. Çelik, Nisa & Seadawy, Aly R. & Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Alipanah, Amjad & Zafari, Mahnaz, 2023. "Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    5. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    6. Yu, Guo-Fu & Tam, Hon-Wah, 2006. "Conservation laws for two (2+1)-dimensional differential–difference systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 189-196.
    7. Moghimi, Mahdi & Hejazi, Fatemeh S.A., 2007. "Variational iteration method for solving generalized Burger–Fisher and Burger equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1756-1761.
    8. Keramati, B., 2009. "An approach to the solution of linear system of equations by He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 152-156.
    9. Demiray, Hilmi, 2006. "Interaction of nonlinear waves governed by Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1185-1189.
    10. Siddiqui, A.M. & Ahmed, M. & Ghori, Q.K., 2007. "Thin film flow of non-Newtonian fluids on a moving belt," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1006-1016.
    11. Shidfar, A. & Molabahrami, A. & Babaei, A. & Yazdanian, A., 2009. "A study on the d-dimensional Schrödinger equation with a power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2154-2158.
    12. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
    13. Mădălina Sofia Paşca & Olivia Bundău & Adina Juratoni & Bogdan Căruntu, 2022. "The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    14. Al-Khaled, Kamel, 2007. "Theory and computation in singular boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 678-684.
    15. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    16. Muhammad Bilal Khan & Eze R. Nwaeze & Cheng-Chi Lee & Hatim Ghazi Zaini & Der-Chyuan Lou & Khalil Hadi Hakami, 2023. "Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates," Mathematics, MDPI, vol. 11(24), pages 1-27, December.
    17. Mei, Shu-Li & Du, Cheng-Jin & Zhang, Sen-Wen, 2008. "Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 536-542.
    18. Biazar, J. & Eslami, M. & Aminikhah, H., 2009. "Application of homotopy perturbation method for systems of Volterra integral equations of the first kind," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3020-3026.
    19. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    20. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.

    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:gam:jmathe:v:10:y:2022:i:4:p:615-:d:751316. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.