A Novel Approach to Time-Fractional Equations using Fuzzy Beta Laplace Transform Iterative Technique and its Applications in Fluid Dynamics

This work proposes a novel approach for modeling complex systems with uncertain data using fuzzy calculus and linear time-fractional differential equations. We provide the fuzzy beta generalized Hukuhara derivative, which maintains inherent uncertainties without transforming fuzzy issues into precise formulations, improving both accuracy and interpretability. We present a fuzzy beta Laplace transform iterative approach to solve fuzzy linear time-fractional equations in fluid dynamics effectively. Case studies, including the fuzzy time-fractional diffusion and advection-dispersion equations, demonstrate the effectiveness of our strategy in capturing system dynamics under uncertainty. This study enhances the amalgamation of fuzzy calculus and fractional modeling, offering a solid foundation for the analysis of uncertain complex systems.