Fuzzy Time-Fractional Advection-Dispersion and Navier-Stokes Equations: A Comprehensive Approach

This paper presents a novel approach for modeling and analyzing complex systems withuncertain data by using fuzzy calculus and time-fractional dierential equations. Specically,we propose the use of the fuzzy Atangana-Baleanu time-fractional derivative with non-singularkernels for fuzzy functions as a suitable fractional derivative type for the qualitative analysis offractional dierential equations in fuzzy space. Additionally, we provide a method for numer-ically solving fuzzy linear time-fractional equations in uid dynamics using the fuzzy Laplacetransform iterative method. The eectiveness and practical relevance of our proposed methodare demonstrated through concrete examples, including the fuzzy time-fractional Advection-Dispersion equation, the fuzzy time-fractional Navier-Stokes equation, and Couette ow .These examples showcase the potential of our method to address real-world problems in uiddynamics and provide a clear illustration of the solution steps involved. Our ndings high-light the importance of considering fuzzy calculus and time-fractional dierential equations inmodeling and analyzing complex systems with uncertain data.

کلیدواژه ها:

The fuzzy Atangana-Baleanu time-fractional derivative ، The fuzzy time-fractional Advection-Dispersion equation ، The fuzzy time-fractional Navier-Stokes equation ، Couette flow