In the recent paper [2], the authors obtained new proofs on the existence and uniqueness of the solution of the Volterra linear equation. Applying their results, in this paper we express the exact and approximate solution of the equation in the field of Mikusi´nski operators, F, which corresponds to an integro–differential equation.

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

A new approach to the formulation and solution of the problem of recovering scene topography from a stereo image pair is presented. The approach circumvents the need to solve the correspondence problem, returning a solution that makes surface interpolation unnecessary. The methodology demonstrates a way of handling image analysis problems that differs from the usual linear-system approach. We e...

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann (Berezin) integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra Gm (i.e., a sought after element of t...

Dual integral equations with trigonometric kernel are reinvestigated here for a solution. The behaviour of one of the integrals at the end points of the interval complementary to the one in which it is defined plays the key role in determining the solution of the dual integral equations. The solution of the dual integral equations is then applied to find an exact solution of the water wave scat...

In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...