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A New Technique For Approximate Solution Of Fractional-Order Partial Differential Equations

Author

Listed:
  • LAIQ ZADA

    (Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan)

  • RASHID NAWAZ

    (Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan)

  • MOHAMMAD A. ALQUDAH

    (��Department of Basic Sciences, School of Basic Sciences and Humanities, German Jordanian University Amman 11180, Jordan)

  • KOTTAKKARAN SOOPPY NISAR

    (��Department of Mathematics, College of Arts and Sciences, Wadi Adawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia)

Abstract

In the present paper, the optimal auxiliary function method (OAFM) has been extended for the first time to fractional-order partial differential equations (FPDEs) with convergence analysis. To find the accuracy of the OAFM, we consider the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations as a test example. The proposed technique has auxiliary functions and convergence control parameters, which accelerate the convergence of the method. The other advantage of this method is that there is no need for a small or large parameter assumption, and it gives an approximate solution after only one iteration. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different FPDEs.

Suggested Citation

  • Laiq Zada & Rashid Nawaz & Mohammad A. Alqudah & Kottakkaran Sooppy Nisar, 2022. "A New Technique For Approximate Solution Of Fractional-Order Partial Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-8, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400151
    DOI: 10.1142/S0218348X22400151
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    Cited by:

    1. Fang, Xing & Qiao, Leijie & Zhang, Fengyang & Sun, Fuming, 2023. "Explore deep network for a class of fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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