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Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel

Author

Listed:
  • Mounirah Areshi
  • Muhammad Naeem
  • Noorolhuda Wyal

Abstract

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate‐analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional‐order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology.

Suggested Citation

  • Mounirah Areshi & Muhammad Naeem & Noorolhuda Wyal, 2022. "Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:7635696
    DOI: 10.1155/2022/7635696
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    References listed on IDEAS

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    1. Hossein Jafari & Jyoti Geetesh Prasad & Pranay Goswami & Ravi Shanker Dubey, 2021. "Solution Of The Local Fractional Generalized Kdv Equation Using Homotopy Analysis Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-10, August.
    2. Hossein Jafari & Hassan Kamil Jassim & Dumitru Baleanu & Yu-Ming Chu, 2021. "On The Approximate Solutions For A System Of Coupled Korteweg–De Vries Equations With Local Fractional Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-7, August.
    3. 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).
    4. 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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