The solving fuzzy franctional differential equations by generalized differention ability

In this thesis the solutions of fuzzy fractional differential equations (FFDEs) under Riemann-Liouville Hdifferentiability (generalized differentionability) by fuzzy Laplace transforms have been studied. So, firstly, we define differentiability, integral and fuzzy initial value problems and then the conditions of existence and having a unique solution are presented. Also the different solutions of fuzzy initial value problems, which are generated by different definitions of fuzzy derivative, are presented. As the fuzzy derivatives and integrals are required for solving the fuzzy differential equations of fractional order, the definitions and properties of fuzzy derivative and integrals are evaluated. In order to solve FFDEs, the fuzzy Laplace transforms of the Riemann-Liouville Hderivative of f,( RLDqa+f(x) are defined. The benefit of L[( RLDqa+f)(x) is that it can be written according to L[f(x)]. Moreover, some illustrative examples are solved to show the efficiency and utility of Laplace transforms method.

Keywords:

Fuzzy fractional differential equations , Fuzzy initial value problem , Riemann-Liouville H-differentiability , Fuzzy Laplace transforms