A reliable algorithm of homotopy analysis method for solving fuzzy integral equations of fractional order

Abstract EN

In this paper, we based on the homotopy analysis method (HAM), a powerful algorithm is developed for the solution of linear and nonlinear fuzzy integral equations of fractional order.

The proposed algorithm presents the procedure of constructing the set of base functions and gives the high-order deformation equation in a simple form.

This method different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h.

The fractional derivative is described in the Caputo sense and the fractional integration is described in the Riemann-Liouville formula.

The analysis is accompanied by some numerical examples to show the accuracy and validity of this approach.