In many mathematical types of research, in order to solve the fuzzy
fractional differential equations, we should transform these problems
into crisp corresponding problems and by solving them the approximate
solution can be obtained. The aim of this paper is to present a new
direct method to solve the fuzzy fractional differential equations
without this transformation. In this work, the fuzzy generalized Taylor
expansion by using the sense of fuzzy Caputo fractional derivative for
fuzzy-valued functions is presented. For solving fuzzy fractional
differential equations, the fuzzy generalized Euler's method is applied.
In order to show the accuracy and efficiency of the presented method,
the local and global truncation errors are determined. Moreover, the
consistency, the convergence and the stability of the generalized
Euler's method are proved in detail. Eventually, the numerical examples,
especially in the switching point case, show the flexibility and the
capability of the presented method.