in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

This article presents a survey of various methods for nonparametric identification of nonlinear systems. Nonparametric identification methods are those that measure Wiener kernels or Volterra kernels, since an output of a nonlinear system can be described by the convolution integral of Wiener or Volterra kernels and the system input. Section 1 highlights the representation methods of nonlinear ...

Keywords: Volterra–Stieltjes integral equation Fractional integral–differential equations Riemann–Liouville fractional operators Existence and stability of solutions Fixed point a b s t r a c t Our aim in this paper is to study the existence and the stability of solutions for Riemann–Liouville Volterra–Stieltjes quadratic integral equations of fractional order. Our results are obtained by using...

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...