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An Approach to Solve Fuzzy Fractional Darboux Problems Under the Caputo Derivative

Author

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  • Nagwa A. Saeed
  • Deepak B. Pachpatte

Abstract

This paper investigates the Fuzzy Adomian Decomposition Method to find approximate analytical solutions for linear and nonlinear fuzzy Darboux problems using the Caputo‐type mixed fractional derivative, which plays an important role in applied and engineering sciences. The solutions are formulated as series with easily calculable terms. Multiple examples are included to illustrate the effectiveness of the approach, which employs the σ‐level representation of fuzzy numbers. The results are presented graphically, depicting both the lower and upper bounds of the solutions.

Suggested Citation

  • Nagwa A. Saeed & Deepak B. Pachpatte, 2025. "An Approach to Solve Fuzzy Fractional Darboux Problems Under the Caputo Derivative," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnijde:v:2025:y:2025:i:1:n:4536339
    DOI: 10.1155/ijde/4536339
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    References listed on IDEAS

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    1. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland & Melike Kaplan, 2022. "Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
    2. Abdullah, & ur Rahman, Ghaus & Gómez-Aguilar, J.F., 2025. "M-shape, lump, homoclinic breather and other soliton interaction of the Landau-Ginzburg-Higgs model in nonlinear fiber optics," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    3. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland, 2022. "Analysis of the Fuzzy Fractional‐Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo‐Fabrizio Derivative," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
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