NONLINEAR BOUNDARY VALUE PROBLEM FOR IMPLICIT DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER IN BANACH SPACES

被引：12

作者：

Benchohra, Mouffak ^{[1
,2
]}

Bouriah, Soufyane ^{[1
]}

Darwish, Mohamed Abdalla ^{[3
,4
]}

机构：

[1] Univ Djillali Liabes Sidi Bel Abbes, Lab Math, POB 89, Sidi Bel Abbes 22000, Algeria

[2] King Abdulaziz Univ, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

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

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

来源：

FIXED POINT THEORY | 2017年 / 18卷 / 02期

关键词：

Boundary value problem; Caputo's fractional derivative; implicit fractional; differential equations in Banach space; fractional integral; existence; Gronwall's lemma for singular kernels; measure of noncompactness; fixed point; DARBOUX PROBLEM;

D O I：

10.24193/fpt-ro.2017.2.36

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. We apply the technique of measure of noncompactness and the fixed point theorems of Darbo and Winch. As an application, two examples are included to show the applicability of our results.

引用

页码：457 / 470

页数：14

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