A Class of Fuzzy Integral Equations and the Existence and Uniqueness of Their Solutions

Abstract

The aim of this paper to presented a class of interesting fuzzy integral nonlinear equations involving nonlinear fuzzy function of other multi fuzzy nonlinear functions that presented in fist time, the formula under study is an interesting type of a fuzzy nonlinear Volterra integral equation which defined on fuzzy numbers that has lower and upper functions. The Housdorf fuzzy metric space on fuzzy numbers and a fuzzy metric space on a fuzzy continuous functions and the space of all uniform modulus of absolutely fuzzy continuous functions have been given in details. Also the observer results investigated on parameter cases of fuzzy problem formulation, some necessary and sufficient conditions of boundedness and locally Lipschitz for different fuzzy functions and differential of them and also using Leibnitz rule for presented fuzzy problem formulation. The locally existence and uniqueness solutions in the space of all uniform modulus of absolutely fuzzy continuous functions which is generalized of fuzzy number space and established on contraction condition which proved by using the properties of fuzzy metric space this certain space. Also used concept of fuzzy Riemann integral and normed function to prove interesting results and illustrated in some examples to clear the proposal fuzzy integral nonlinear equations has a solution in certain fuzzy space that in firstly explained with different metrics spaces and normed properties and satisfied all the hypothesis for the component of the equation and obtain the estimations of the suggested conditions on certain fuzzy metrics as a stuffiest condition for grantee the assuming equations has a fuzzy solution with their lower and upper parameters.