Numerical Solutions of Fuzzy Linear Fractional Differential Equations With Laplace Transforms Under Caputo-Type H-Differentiability - Ekhtiar Khodadadi; Mesut Karabacak; Ercan Çelik (Journal of Mathematics)
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+βCyx. 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.