scholarly journals To Theory One Class Linear Model Noclassical Volterra Type Integral Equation with Left Boundary Singular Point

2013 ◽  
Vol 04 (09) ◽  
pp. 1301-1312
Author(s):  
Nusrat Rajabov
Keyword(s):  
Integral Equation ◽  
Singular Point ◽  
Linear Model ◽  
Volterra Type ◽  
Left Boundary ◽  
Type Integral

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

A volterra-type integral equation

1989 ◽  
Vol 40 (4) ◽  
pp. 438-442 ◽  
Author(s):  
S. Ashirov ◽  
Ya. D. Mamedov
Keyword(s):  
Integral Equation ◽  
Volterra Type ◽  
Type Integral

Numerical Scheme for the Solution of Fractional Differential Equations of Order Greater Than One

2005 ◽  
Vol 1 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Pankaj Kumar ◽  
Om P. Agrawal
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Volterra Type ◽  
Entire Domain ◽  
Type Integral ◽  
Fractional Differential

This paper presents a numerical scheme for the solutions of Fractional Differential Equations (FDEs) of order α, 1<α<2 which have been expressed in terms of Caputo Fractional Derivative (FD). In this scheme, the properties of the Caputo derivative are used to reduce an FDE into a Volterra-type integral equation. The entire domain is divided into several small domains, and the distribution of the unknown function over the domain is expressed in terms of the function values and its slopes at the node points. These approximations are then substituted into the Volterra-type integral equation to reduce it to algebraic equations. Since the method enforces the continuity of variables at the node points, it provides a solution that is continuous and with a slope that is also continuous over the entire domain. The method is used to solve two problems, linear and nonlinear, using two different types of polynomials, cubic order and fractional order. Results obtained using both types of polynomials agree well with the analytical results for problem 1 and the numerical results obtained using another scheme for problem 2. However, the fractional order polynomials give more accurate results than the cubic order polynomials do. This suggests that for the numerical solutions of FDEs fractional order polynomials may be more suitable than the integer order polynomials. A series of numerical studies suggests that the algorithm is stable.

scholarly journals Data dependence of solutions for Fredholm-Volterra integral equations in L2[a, b]

2013 ◽  
Vol 5 (1) ◽  
pp. 5-19
Author(s):  
Szilárd András
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Continuous Dependence ◽  
Main Tool ◽  
Volterra Integral Equations ◽  
Data Dependence ◽  
Solution Operator ◽  
Volterra Type ◽  
Type Integral

Abstract In this paper we study the continuous dependence and the differentiability with respect to the parameter λ ∈ [λ1, λ2] of the solution operator S : [λ1, λ2] → L2[a, b] for a mixed Fredholm-Volterra type integral equation. The main tool is the fiber Picard operators theorem (see [9], [8], [11], [3] and [2]).

scholarly journals On nontrivial solvability of a nonlinear Hammerstein-Volterra type integral equation

2012 ◽  
Author(s):  
С.А. Григорян ◽  
Х.А. Хачатрян
Keyword(s):  
Integral Equation ◽  
Volterra Type ◽  
Type Integral

В настоящей заметке исследуется вопрос о существовании однопараметрического семейства положительных и ограниченных решений для одного класса нелинейных однородных интегральных уравнений типа Гаммерштейна - Вольтерра. Указанный класс уравнений имеет важное применение в кинетической теории газов.

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