Atefeh Armand - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Tofigh Allahviranloo - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Saeid Abbasbandy - Imam Khomeini Int. University
Zeinab Gouyandeh - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

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

Generalized Hukuhara derivative, Caputo generalized Hukuhara derivative, Fuzzy mean value theorem for Riemann-Liouville integral, Generalized Taylor’s expansion, Fuzzy fractional differential equations, Fuzzy fractional Euler’s method