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Numerical Solutions of Fuzzy Linear Fractional Differential Equations With Laplace Transforms Under Caputo‐Type H‐Differentiability

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  • Ekhtiar Khodadadi
  • Mesut Karabacak
  • Ercan Çelik

Abstract

In this article, we explored the numerical solution of fuzzy linear fractional differential equations (FLFDEs) under Caputo‐type H‐differentiability. To obtain a numerical solution, it is crucial to understand the fuzzy Laplace transform of the Caputo‐type H‐derivative of Da+β Cyx. We provided a detailed explanation of how to obtain the fuzzy Laplace transform from this fractional function under Caputo‐type H‐differentiability. To demonstrate the applicability of our proposed approach, we presented solutions to real‐world problems. These solutions exhibit the usefulness and effectiveness of our method in providing accurate and reliable solutions to FLFDEs. Also, we analyzed the performance of the method and discussed potential computational limitations, particularly for highly oscillatory or discontinuous solutions. Our approach can potentially provide insights into various areas such as engineering, physics, and biology, where FLFDEs play a significant role in modeling complex systems. The numerical examples include three‐dimensional graphical representations of approximate fuzzy solutions with the graph of exact solutions, facilitating a direct visual comparison.

Suggested Citation

  • Ekhtiar Khodadadi & Mesut Karabacak & Ercan Çelik, 2025. "Numerical Solutions of Fuzzy Linear Fractional Differential Equations With Laplace Transforms Under Caputo‐Type H‐Differentiability," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:9998269
    DOI: 10.1155/jom/9998269
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    References listed on IDEAS

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    1. T. Allahviranloo & S. Abbasbandy & M. R. Balooch Shahryari & S. Salahshour & D. Baleanu, 2013. "On Solutions of Linear Fractional Differential Equations with Uncertainty," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, November.
    2. Kamran Kamran & Zahir Shah & Poom Kumam & Nasser Aedh Alreshidi, 2020. "A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
    3. T. Allahviranloo & S. Abbasbandy & M. R. Balooch Shahryari & S. Salahshour & D. Baleanu, 2013. "On Solutions of Linear Fractional Differential Equations with Uncertainty," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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