The fuzzy generalized Taylor’s expansion with application in fractional differential equations

In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzy fractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessary that we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractional differential equations in the sense of Caputo differentiability. The effectiveness of the proposed method is verified by three examples.