Fuzzy differential and integral equations have been studied by many authors [1, 2, 5, 6, 7, 14]. Kaleva [5] discussed the properties of differentiable fuzzy set-valued mappings by means of the concept of H-differentiability introduced by Puri and Ralescu [9]. Seikkala [11] defined the fuzzy derivative which is a generalization of the Hukuhara derivative [9] and the fuzzy integral which is the s...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has...

The integral equation method is widely used for solving many problems in mathematical physics and engineering. This article proposes a computational method for solving nonlinear Fredholm-Volterra integral equations. Several numerical methods for approximating the solution of linear and nonlinear integral equations and specially FredholmVolterra integral equations are known [1-10]. Also, BlockPu...

In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and si...

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, ...