Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem

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 β∈(0,1)β∈0,1. Solving two examples of linear and nonlinear FFIVP illustrates the method.

► Defining the Caputo-type fuzzy fractional derivatives. ► Solving Fuzzy Fractional Initial Value Problem under the Caputo-type fuzzy fractional derivatives. ► Description of the modified fractional Euler method in fuzzy context.