11 research outputs found
Approximate Solution of Volterra-Stieltjes Linear Integral Equations of the Second Kind with the Generalized Trapezoid Rule
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
Asymptotic solutions of forced nonlinear second order differential equations and their extensions
Using a modified version of Schauder's fixed point theorem, measures of
non-compactness and classical techniques, we provide new general results on the
asymptotic behavior and the non-oscillation of second order scalar nonlinear
differential equations on a half-axis. In addition, we extend the methods and
present new similar results for integral equations and Volterra-Stieltjes
integral equations, a framework whose benefits include the unification of
second order difference and differential equations. In so doing, we enlarge the
class of nonlinearities and in some cases remove the distinction between
superlinear, sublinear, and linear differential equations that is normally
found in the literature. An update of papers, past and present, in the theory
of Volterra-Stieltjes integral equations is also presented
Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
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.publishe
Global Asymptotic Stability for Nonlinear Functional Integral Equation of Mixed Type
The existence results of global asymptotic stability of the solution are proved for
functional integral equation of mixed type. The measure of noncompactness and the fixed-point
theorem of Darbo are the main tools in carrying out our proof. Furthermore, some examples are
given to show the efficiency and usefulness of the main findings