Fuzzy Fractional Calculus: A Comprehensive Overview with a Focus on weighted Caputo-type generalized Hukuhara Differentiability and Analytical Solutions for Fuzzy Fractional Differential Equations

Document Type : Research Paper

Authors

1 Islamic Azad University, karaj branch

2 Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

This paper introduces a novel approach to obtaining analytical solutions for
fuzzy fractional differential equations in the context of weighted Caputo-type generalized
Hukuhara derivatives. The paper proposes the use of non-singular kernels to improve the
accuracy of fractional calculus in fuzzy space and establishes the uniqueness of solutions for
fuzzy fractional differential equations. The paper also introduces the concept of fuzzy Laplace
transforms to facilitate the solution of these equations. Practical examples, such as the fuzzy
fractional Newton’s law of heating and cooling, are provided to demonstrate the effectiveness
of the proposed method. Overall, this paper contributes to the development of practical solutions
for real-world problems in fuzzy space and enhances the accuracy of fractional calculus
in this context.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 2
March and April 2024
Pages 19-34

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