Applying the fuzzy homotopy analysis method to solve fuzzy initial value problems with variable coefficients

Abstract

In this study, we applied the fuzzy homotopy analysis method to find an approximate but analytical solution to initial value problems that have fuzzy variable coefficients. These coefficients were represented by triangular fuzzy functions. This approach lets us solve the fuzzy differential equations as an endless series of fuzzy numbers, where each fuzzy component can be determined without much difficulty. Based on the numerical data we analyzed, the series solutions we arrived at are both precise and closely match the exact analytical solutions for fuzzy problems.