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 forfuzzy fractional differential equations in the context of weighted Caputo-type generalizedHukuhara derivatives. The paper proposes the use of non-singular kernels to improve theaccuracy of fractional calculus in fuzzy space and establishes the uniqueness of solutions forfuzzy fractional differential equations. The paper also introduces the concept of fuzzy Laplacetransforms to facilitate the solution of these equations. Practical examples, such as the fuzzyfractional Newton’s law of heating and cooling, are provided to demonstrate the effectivenessof the proposed method. Overall, this paper contributes to the development of practical solutionsfor real-world problems in fuzzy space and enhances the accuracy of fractional calculusin this context.