Method of Boundary Integral Equations with Hypersingular Integrals in Boundary-Value Problems

Computation of singular and hypersingular boundary integrals by Green identity and application to boundary value problems

The problem of computing singular and hypersingular integrals involved in a large class of boundary value problems is considered. The method is based on Green’s theorem for calculating the diagonal elements of the resulting discretized matrix using the Nyström discretization method. The method is successfully applied to classical boundary value problems. Convergence of the method is also discus...

Hypersingular nonlinear boundary-value problems with a small parameter

For the first time, some hypersingular nonlinear boundary-value problems with a small parameter ε at the highest derivative are described. These problems essentially (qualitatively and quantitatively) differ from the usual linear and quasilinear singularly perturbed boundary-value problems and have the following unusual properties: (i) in hypersingular boundary-value problems, super thin bounda...

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Fuzzy Solutions for Boundary Value Problems with Integral Boundary Conditions

The Banach fixed point theorem is used to investigate the existence and uniquenness of fuzzy solutions for a class of second order nonlinear boundary value problems with integral boundary conditions.

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions