Abstract
We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed.
Highlights
In the theory of integral equations and their numerous applications, one can encounter some classes of integral equations having an important significance
We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdelyi-Kober type
This fact is mainly connected with applications of the mentioned classes of integral equations to the description of several real world events which appear in engineering, mechanics, physics, mathematical physics, electrochemistry, bioengineering, porous media, viscoelasticity, control theory, transport theory, kinetic theory of gases, radiative transfer, and other important branches of exact science and applied mathematics
Summary
We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdelyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be discussed
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