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.


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