On a quadratic integral equation with supremum involving Erdelyi-Kober fractional order

被引：22

作者：

Darwish, Mohamed Abdalla ^{[1
,2
]}

Sadarangani, Kishin ^{[3
]}

机构：

[1] King Abdulaziz Univ, Sci Fac Girls, Dept Math, Jeddah 21413, Saudi Arabia

[2] Damanhour Univ, Fac Sci, Dept Math, Damanhour, Egypt

[3] Univ Las Palmas Gran Canaria, Dept Matemat, Baja 35017, Las Palmas De G, Spain

来源：

MATHEMATISCHE NACHRICHTEN | 2015年 / 288卷 / 5-6期

关键词：

Quadratic integral equation; fractional calculus; Erdelyi-Kober; measure of noncompactness; Darbo's fixed point theorem; supremum; 45G10; 47H09; 45M99; MONOTONIC SOLUTIONS;

D O I：

10.1002/mana.201400063

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce Erdelyi-Kober fractional quadratic integral equation with supremum, namely (0,1). This equation contains as special cases numerous integral equations studied by other authors. We show that there exists at least one monotonic solution belonging to C[0, 1] of our equation. The main tools in our analysis are Darbo fixed point theorem and the measure of noncompactness related to monotonicity which was introduced by Bana and Olszowy. Finally, we present an example for illustrating the natural realizations of our abstract results.

引用

页码：566 / 576

页数：11

共 19 条

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Alamo J.A., 1994, Serdica Bulg. Math. Publ., V20, P351

[2] Monotonic solutions of a quadratic integral equation of Volterra type [J].