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Analysis Of The Conformable Temporal-Fractional Swift–Hohenberg Equation Using A Novel Computational Technique

Author

Listed:
  • AZIZ KHAN

    (Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia)

  • MUHAMMAD IMRAN LIAQAT

    (��National College of Business Administration & Economics, Lahore, Pakistan)

  • MANAR A. ALQUDAH

    (��Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia)

  • THABET ABDELJAWAD

    (Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia§Department of Medical Research, China Medical University, Taichung 40402, Taiwan¶Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea)

Abstract

The main objective of this study is to provide a new computational procedure for extracting approximate and exact solutions of the temporal-fractional Swift–Hohenberg (S–H) equations in the context of conformable derivatives using the conformable natural transform (CNT) and Daftardar–Jafari method (DJM). We refer to it as the “natural conformable Daftardar–Jafari method†(CNDJM). The three types of errors are assessed in order to gauge the efficiency and consistency of the proposed method. Furthermore, 2D and 3D graphics are used to compare the exact and approximate solutions. This method offers a considerable benefit over homotopy analysis and Adomian decomposition methods in terms of computational work because it does not require Adomian and He’s polynomials. The procedure is quick and easy to use.

Suggested Citation

  • Aziz Khan & Muhammad Imran Liaqat & Manar A. Alqudah & Thabet Abdeljawad, 2023. "Analysis Of The Conformable Temporal-Fractional Swift–Hohenberg Equation Using A Novel Computational Technique," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-17.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400509
    DOI: 10.1142/S0218348X23400509
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    Cited by:

    1. Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative," Mathematics, MDPI, vol. 12(7), pages 1-21, March.

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