Allahviranloo, TofighNoeiaghdam, ZahraNoeiaghdam, SamadNieto Roig, Juan José2020-12-162020-12-162020Allahviranloo, T.; Noeiaghdam, Z.; Noeiaghdam, S.; Nieto, J.J. A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion. Mathematics 2020, 8, 2166http://hdl.handle.net/10347/24014In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and 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 introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and 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 methodeng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Fuzzy fractional differential equationsGeneralized fuzzy Taylor expansionGeneralized fuzzy Euler’s methodGlobal truncation errorLocal truncation errorConvergenceStabilityjournal article10.3390/math81221662227-7390open access