Approximate Solution of Volterra-Stieltjes Linear Integral Equations of the Second Kind with the Generalized Trapezoid Rule

Avıt ASANOV | Elman HAZAR | Kalıskan MATANOVA

The numerical solution of linear Volterra-Stieltjes integral equations of the second kind by using the generalized trapezoid rule is established and investigated. Also, the conditions on estimation of the error are determined and proved. A selected example is solved employing the proposed method.

A class of systems of linear Fredholm integral equations of the third kind

Avıt ASANOV

Solutions to systems of linear Fredholm integral equations of the third kind

Avıt ASANOV

Fractional differential equations and Volterra–Stieltjes integral equations of the second kind

Avıt ASANOV

In this paper, we construct a method to find approximate solutions to fractional differential equations involving fractional derivatives with respect to another function. The method is based on an equivalence relation between the fractional differential equation and the Volterra-Stieltjes integral equation of the second kind. The generalized midpoint rule is applied to solve numerically the integral equation and an estimation for the error is given. Results of numerical experiments demonstrate that satisfactory and reliable results could be obtained by the proposed method.

On a Class of Systems of Linear and Nonlinear Fredholm Integral Equations of the Third Kind with Multipoint Singularities

Avıt ASANOV

Based on a new approach, we show that finding solutions for a class of systems of linear (respectively, nonlinear) Fredholm integral equations of the third kind with multipoint singularities is equivalent to finding solutions of systems of linear (respectively, nonlinear) Fredholm integral equations of the second kind with additional conditions. We study the existence, nonexistence, uniqueness, and nonuniqueness of solutions for this class of systems of Fredholm integral equations of the third kind with multipoint singularities.

A class of linear and nonlinear Fredholm integral equations of the third kind

Avıt ASANOV | Kalıskan MATANOVA

In this paper we are applying a new approach to prove the uniqueness and existence theorems for linear and nonlinear Fredholm integral equations of the third kind.

Solutions to systems of linear Fredholm integral equations of the third kind with multipoint singularities

Avıt ASANOV

A new approach is used to show that the solution for one class of systems of linear Fredholm integral equations of the third kind with multipoint singularities is equivalent to the solution of systems of linear Fredholm integral equations of the second kind with additional conditions. The existence, nonexistence, uniqueness, and nonuniqueness of solutions to systems of linear Fredholm integral equations of the third kind with multipoint singularities are analyzed

On numerical solution of the second-order linear Fredholm-Stieltjes integral equation

Avıt ASANOV

In this framework, the necessary and sufficient conditions for the existence and uniqueness of the second-order linear Fredholm-Stieltjes-integral equations, u(x) = lambda integral(b)(a) K(x, y) u(y) dg(y) + f(x), x is an element of[a, b], are thoroughly derived. Moreover, instead of approximating the integral equation by different numbers of partition n, the optimal number n for the given error tolerance is established. The system of equations is implemented in MAPLE for the Runge method. An efficient scheme is proposed for second-order integral equations. The solution has been compared with ...More

On One Class of Nonclassical Linear Volterra Integral Equations of the First Kind

Avıt ASANOV

On the basis of a new approach, we prove the uniqueness theorem and construct Lavrent'ev's regularizing operators for the solution of nonclassical linear Volterra integral equations of the first kind with nondifferentiable kernels.

One Class of Systems of Linear Fredholm Integral Equations of the Third Kind on the Real Line with Multipoint Singularities

Avıt ASANOV

Using a modification of the approach previously developed by the authors, we show that finding solutions of one class of systems of linear Fredholm integral equations of the third kind on the real line with finitely many multipoint singularities is equivalent to finding solutions of a system of linear Fredholm integral equations of the second kind on the real line with additional conditions imposed on the kernels and the free term. The existence, nonexistence, uniqueness, and nonuniqueness of solutions of systems in this class are studied.