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

Document Type : Research Paper

Authors

1 Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran

2 IAU- Karaj Branch

3 Islamic Azad university

4 Islamic Azad University

5 Islamic Azad University, karaj branch

Abstract

This paper presents a novel approach for modeling and analyzing complex systems with
uncertain data by using fuzzy calculus and time-fractional di erential equations. Speci cally,
we propose the use of the fuzzy Atangana-Baleanu time-fractional derivative with non-singular
kernels for fuzzy functions as a suitable fractional derivative type for the qualitative analysis of
fractional di erential equations in fuzzy space. Additionally, we provide a method for numer-
ically solving fuzzy linear time-fractional equations in
uid dynamics using the fuzzy Laplace
transform iterative method. The e ectiveness and practical relevance of our proposed method
are 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
uid
dynamics and provide a clear illustration of the solution steps involved. Our ndings high-
light the importance of considering fuzzy calculus and time-fractional di erential equations in
modeling and analyzing complex systems with uncertain data.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 5
September and October 2024
Pages 105-119

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