Analysis of semi-analytical method for solving fuzzy fractional differential equations with strongly nonlinearity under caputo derivative sense.

Fractional differential equations with strong nonlinearity are important in modelling complex physical phenomena. Therefore, there is an urgent need to employ new technique to help researches and physicists to understand the physical problems better and to deal with such equations. In this paper, we develop and analyze a semi-analytical technique called the homotopy analysis method (HAM) which solve first order fuzzy fractional differential equation with strong nonlinearity under Caputo derivative sense by adjusting the convergence of the series solution. The paper also presents the fuzzy formulation of the proposed HAM using the concepts of fuzzy set theory combined with the properties of fractional calculus and analyzed it in order to obtain the semi-analytical solution. The feasibility of the technique is presented by solving an example of first order nonlinear fractional fuzzy initial value problem (NFFIVP). Finally, the numerical results show that the applied technique is accurate and reliable in solving first order NFFIVP. Thus, the proposed HAM can be extended to treat more general fuzzy fractional order models in physics and engineering. [ABSTRACT FROM AUTHOR]