In this paper, the Cauchy problem of fuzzy fractional differential equations Tγut=Ftut, ut0=u0, with fuzzy conformable fractional derivative (γ-differentiability, where γ∈01) are introduced. We study the existence and uniqueness of solutions and approximate solutions for the fuzzy-valued mappings of a real variable, we prove some results by applying the embedding theorem, and the properties of the fuzzy solution are investigated and developed. Also, we show the relation between a solution and its approximate solutions to the fuzzy fractional differential equations of order γ.
Part of the book: Fuzzy Systems
The notion of inclusion by generalized conformable differentiability is used to analyze fuzzy conformable differential equations (FCDE). This idea is based on expanding the class of conformable differentiable fuzzy mappings, and we use generalized lateral conformable derivatives to do so. We’ll see that both conformable derivatives are distinct and that they lead to different FCDE solutions. The approach’s utility and efficiency are demonstrated with an example.
Part of the book: Qualitative and Computational Aspects of Dynamical Systems