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Analysis of Fractional Differential Equations with the Help of Different Operators

Author

Listed:
  • Naveed Iqbal
  • Moteb Fheed Saad Al Harbi
  • Saleh Alshammari
  • Shamsullah Zaland

Abstract

This study uses an Elzaki decomposition method with two fractional derivatives to solve a fractional nonlinear coupled system of Whitham‐Broer‐Kaup equations. For the fractional derivatives, we used Caputo and Atangana‐Baleanu derivatives in the Caputo manner. Furthermore, the proposed techniques are compared to the solutions of other renowned analytical methods, including the Adomian decomposition technique, variation iteration technique, and homotopy perturbation technique. We used two nonlinear problems to illustrate the accuracy and validity of the proposed approaches. The results of numerical simulations were used to verify that the proposed methods are accurate and efficient, and the results are displayed in graphs and tables. The obtained results demonstrate that the algorithm is very real, simple to apply, and effective in investigating the nature of complicated nonlinear models in science and engineering.

Suggested Citation

  • Naveed Iqbal & Moteb Fheed Saad Al Harbi & Saleh Alshammari & Shamsullah Zaland, 2022. "Analysis of Fractional Differential Equations with the Help of Different Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:1333109
    DOI: 10.1155/2022/1333109
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    References listed on IDEAS

    as
    1. Noufe H. Aljahdaly & Ali Akgül & Rasool Shah & Ibrahim Mahariq & Jeevan Kafle, 2022. "A Comparative Analysis of the Fractional‐Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Rabab Alyusof & Shams Alyusof & Naveed Iqbal & Mohammad Asif Arefin, 2022. "Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential‐Decay Kernel," Complexity, John Wiley & Sons, vol. 2022(1).
    3. 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.
    4. Rabab Alyusof & Shams Alyusof & Naveed Iqbal & Mohammad Asif Arefin & Fathalla A. Rihan, 2022. "Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential-Decay Kernel," Complexity, Hindawi, vol. 2022, pages 1-14, May.
    5. 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.
    6. Shailesh A. Bhanotar & Mohammed K. A. Kaabar, 2021. "Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-18, August.
    7. Noufe H. Aljahdaly & Ali Akgül & Rasool Shah & Ibrahim Mahariq & Jeevan Kafle & A. Ghareeb, 2022. "A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law," Journal of Mathematics, Hindawi, vol. 2022, pages 1-30, February.
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