A Study of Some Fuzzy Fractional Differential Equations

Abstract

In this dissertation, we present the study of some fuzzy fractional differential equations, in the first one, we prove that fuzzy fractional differential equation is equivalent to the fuzzy integral equation and then using this equivalence existence and uniqueness result is establish. Fuzzy derivative is consider in the GoetschelVoxman sense and fractional derivative is consider in the Riemann Liouville sense. Also we give some applications of the main result. Secondly the work is concerned with the existence and uniqueness of solutions of fuzzy fractional differential equations using fixed point theory. We provide some results answering when we can expect a solution of the problem. Thirdly we primarily focused on the existence and uniqueness of the initial value problem for fractional order fuzzy ordinary differential equations in a fuzzy metric space.