Hybrid Fuzzy Differential Equations and Different Numerical Solutions

Abstract

In this thesis, hybrid fuzzy differential equations (HFDEs) are considered and solved under Hukuhara derivative by several numerical methods. We study hybrid fuzzy differential equations with different fuzzy initial conditions using different types of fuzzy numbers (triangular, trapezoidal and triangular shaped fuzzy numbers). To the best of our knowledge, it is the first time to use trapezoidal and triangular shaped fuzzy numbers as initial conditions. We have solved the HFDE’s under generalized Hakuhara using different numerical methods with a model to illustrate each methods. A Matlab code was built for each of the methods to find the exact solution and to approximate the solution numerically and represent it graphically. Finally, accurate results were obtained for most numerical methods used with different types of fuzzy numbers as initial conditions.