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Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation

El-Sayed Ahmed M. A., Omar Yasmin M. Y.

Demonstratio Mathematica

2021

Vol. 54, nr 1

25--36

In this work, we study the existence of one and exactly one solution x ∈ C[0, 1], for a delay quadratic integral equation of Volterra-Stieltjes type. As special cases we study a delay quadratic integral equation of fractional order and a Chandrasekhar cubic integral equation.

A nonstandard Volterra integral equation on time scales

Reinfelds Andrejs, Christian Shraddha

Demonstratio Mathematica

2019

Vol. 52, nr 1

503--510

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type

Shiri B., Shahmorad S., Hojjati G.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 2

341--355

In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.

Approximate solutions of a certain second order integrodifferential equation

Pachpatte B. G.

Fasciculi Mathematici

2010

Nr 45

99-109

The main aim of this paper is to study the approximate solutions of a certain second order Volterra type integrodifferential equation with given initial values. A variant of a certain basic integral inequality with explicit estimate is used to establish the results.