Existence and Uniqueness of Solution of Volterra Integral Equations
نویسندگان
چکیده
The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of Zadeh, showed that the fuzzy initial value problem x′(t) = f(t, x(t)), x(0) = x0 has a unique fuzzy solution when f satisfies the generalized Lipschitz condition which guarantees a unique solution of the deterministic initial value problem.Kaleva [3] studied the Cauchy problem of fuzzy differential equation, characterized those subsets of fuzzy sets in which the peano theorem is valid.Park et al. in [5] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam in [9] have proved the existence of solution of fuzzy functional equations.
منابع مشابه
Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations
In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.
متن کاملExistence and uniqueness of the solution of fuzzy-valued integral equations of mixed type
In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.
متن کاملNonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution
This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...
متن کاملNumerical Solution of Interval Volterra-Fredholm-Hammerstein Integral Equations via Interval Legendre Wavelets Method
In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...
متن کاملOn existence and uniqueness of solutions of a nonlinear Volterra-Fredholm integral equation
In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we give an example to illustrate the applications of our results.
متن کاملConvergence of Numerical Method For the Solution of Nonlinear Delay Volterra Integral Equations
In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...
متن کامل