ON A CERTAIN ITERATED MIXED INTEGRAL EQUATION

On A Certain Modified Mixed Summation-Integral Type Operator

The Solution of a Certain General Type of Integral Equation.

4For n = 1, the nearest approach to the process used here seems to be found in H. J. S. Smith's Report on the Theory of Numbers, Collected Works, Vol. I, 271-272, Oxford (1894); reproduced by P. Bachmann, Die Lehre von der Kreisteilung, 279-281, Leipzig and Berlin (1921). However, our number yt of (1) for n = 1 is not exhibited explicitly by them in terms of the a's alone, but is defined by mea...

A Certain Integral-recurrence Equation with Discrete-continuous Auto-convolution

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

1 Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Ibb University, P.O. Box 70270, Ibb, Yemen 3 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia 4 Ibnu Sina Institute for Fundamental Science Studies, Universiti Tek...