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Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative

Author

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  • Fareeha Sami Khan
  • M. Khalid
  • Omar Bazighifan
  • A. El-Mesady

Abstract

In this paper, DSEK model with fractional derivatives of the Atangana‐Baleanu Caputo (ABC) is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam‐Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α ∈ (0,1] and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h.

Suggested Citation

  • Fareeha Sami Khan & M. Khalid & Omar Bazighifan & A. El-Mesady, 2022. "Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:4475491
    DOI: 10.1155/2022/4475491
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    References listed on IDEAS

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    2. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional-Order Biological Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, August.
    3. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional‐Order Biological Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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