Existence and uniqueness theorem for fuzzy fractional integralequations with the fuzzy caputo fractional derivative by usingAdomians decomposition method (ADM)

We present on existence and uniqueness theorem for integral equation of fractional order in volvingfuzzy set value mayping of a real variable whose values are normal , convex , upper , semicontinuous ,and compactly sufforted fuzzy sets in n IR ir , we establish condition for aclass of initial value froblemfor impulsive frac tional antegrab inclusion involving the caputofractionalderivative. The Adomiandecomposition method and thehomotopy Perturbation method are twopowerful method whichConsider the approximate Solution of a nonlinear Equation as an infinite Series usually Converging tothe accurate solution , This paper introduces the homotopy perturbation method for overcomingcompletely the disadvantage, The solution procedure is very effective and straight forward. That twomethod are equivalent in solving nonlinear equations

Keywords:

Fuzzy Fractionaldifferentialequations , Caputo fractionalderivative , Fuzzy FractionalSolution , Existence anduniqueness