In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

The analysis of elastic wave propagation and scattering is an important issue in fields such as earthquake engineering, nondestructive testing, and exploration for energy resources. Since the 1980s, the boundary integral equation method has played an important role in the analysis of both forward and inverse scattering problems. For example, Colton and Kress (1998) presented a survey of a vast ...

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the ...

We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functional integral equation of mixed type has solutions being continuous and bounded on the interval [...