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

نویسندگان
Allahviranloo, Tofigh ID 1
Gouyandeh, Zeinab ID 2
Armand, Atefeh ID 3
Abbasbandy, Saeid ID 4

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

4 Imam Khomeini Int. University

doi
10.22111/ijfs.2019.4542
چکیده

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.

کلیدواژه‌ها
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