Differential and integral equations with Henstock–Kurzweil integrable functions

Solving optimal control problems with integral equations or integral equations - differential with the help of cubic B-spline scaling functions and wavelets

In this paper, a numerical method based on cubic B-spline scaling functions and wavelets for solving optimal control problems with the dynamical system of the integral equation or the differential-integral equation is discussed. The Operational matrices of derivative and integration of the product of two cubic B-spline wavelet vectors, collocation method and Gauss-Legendre integration rule for ...

The distributional Henstock-Kurzweil integral and measure differential equations

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...

Differential equations and integral geometry

be the operator of mean value over a radius r sphere centered at y ∈ R. The integral transform I is clearly injective. Let C be a compact hypersurface in R isotopic to a sphere. Theorem 1.1 Let f(x) be a smooth function vanishing near C. Then one can recover f from its mean values along the spheres tangent to C, and the inversion is given by an explicit formula. In fact we will show that this t...

Ordinary Differential Equations and Integrable Models

We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.

Integral geometry and differential equations