## Modified fractional Euler method for solving fuzzy fractional initial value problem.(English)Zbl 1253.35208

Commun. Nonlinear Sci. Numer. Simul. 18, No. 1, 12-21 (2013); corrigendum ibid. 26, No. 1-3, 276-277 (2015).
Summary: In this paper, the solution to fuzzy fractional initial value problem [FFIVP] under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylor’s formula and a modified trapezoidal rule is used for solving initial value problem under fuzzy fractional differential equation of order $$\beta \in (0,1)$$. Solving two examples of linear and nonlinear FFIVP illustrates the method.

### MSC:

 35R13 Fuzzy partial differential equations 35R11 Fractional partial differential equations
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