Fractional relaxation-oscillation differential equations via fuzzy variational iteration method

The fuzzy variation iteration method is investigated to solve a linear fractional differential equation under Caputo generalized Hukuhara differentiability. This method is based on the use of Lagrange multipliers for identification of optimal value in the correction functionals by using fuzzy integration by parts. In this scheme, the correction, functional can make without converting fuzzy fractional differential equation to two crisp equations. To this, derivative of the product of two functions and integration by parts is obtained for fuzzy valued functions. The effectiveness of the proposed method is verified by solving two of the important applications of these equations are fractional relaxation and oscillation differential equations.