Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation
type: Item
instance of: scholarly article
title: Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation
zbMATH Open document ID: 1475.45008
author: A. M. A. El-Sayed
author: Yasmin M. Y. Omar
published in: Demonstratio Mathematica
publication date: 2021-06-01T00:00:00Z
review text: In this paper, the following quadratic integral equation of Volterra-Stieltjes type is studied: \[ x(t)=a(t)+\int\limits_{0}^{\varphi(t)}f_1(t,s,x(s))d_sg_1(t,s)\int\limits_{0}^{1}f_2(t,s,x(s))d_sg_2(t,s), \quad t\in[0,1]. \] The authors discuss the existence of solutions of this equation in the class of continuous functions and the continuous dependence of its unique solution on the functions \(g_1\), \(g_2\) and \(\varphi\). The obtained results are then applied to the fractional-order quadratic integral equation \[ x(t)=a(t)+I^{\alpha}f_1(t,s,x)\cdot\int\limits_{0}^{1}\frac{t}{t+s}f_2(t,s,x(s))ds \] and to the Chandrasekhar quadratic and cubic integral equations \[ x(t)=a(t)+x^p(t)\cdot\int\limits_{0}^{1}\frac{t}{t+s}a(s)x(s)ds, \quad p=1,2. \]
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7353411
zbMATH Keywords: Volterra-Stieltjes type integral equations
zbMATH Keywords: functional integral equations
zbMATH Keywords: existence
zbMATH Keywords: continuous solution
zbMATH Keywords: continuous dependence
reviewed by: Alexander N. Tynda
MaRDI profile type: Publication
full work available at URL: dema-2021-0003
OpenAlex ID: W3140490222
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DOI: 10.1515/DEMA-2021-0003
description: scientific article; zbMATH DE number 7353411