Fuzzy fractional calculus: A comprehensive overview with a focus on weighted Caputo-type generalized Hukuhara differentiability and analytical solutions for fuzzy fractional differential equations

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.