Monotonic solutions for a quadratic integral equation of fractional order

被引：10
|
作者：
El-Sayed, A. M. A. [1 ]
Al-Issa, Sh M. [2 ,3 ]
机构：
[1] Alexandria Univ, Fac Sci, Alexandria, Egypt
[2] Lebanese Int Univ, Fac Sci, Beirut, Lebanon
[3] Int Univ Beirut, Fac Sci, Beirut, Lebanon
来源：
AIMS MATHEMATICS | 2019年 / 4卷 / 03期
关键词：
fractional calculus; quadratic integral equation; fixed point theory; measure of noncompactness;
D O I：
10.3934/math.2019.3.821
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we present a global existence theorem of a positive monotonic integrable solution for the mixed type nonlinear quadratic integral equation of fractional order x(t) = p(t) + h(t, x(t)) integral(t)(0) k(t, s)(f(1)(s, I-alpha f(2)(s, x(s))) + g(1)(s, I-beta g(2)(s, x(s))))ds, t is an element of[0, 1], alpha,beta > 0 by applying the technique of measures of weak noncompactness. As an application, we consider an initial value problem of arbitrary (fractional) order differential equations.
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页码：821 / 830
页数：10
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