Boundary Value Problems for Nonlinear Implicit Caputo-Hadamard-Type Fractional Differential Equations with Impulses

被引：26

作者：

Benchohra, Mouffak ^{[1
,2
]}

Bouriah, Soufyane ^{[1
]}

Graef, John R. ^{[3
]}

机构：

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

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

[3] Univ Tennessee Chattanooga, Dept Math, Chattanooga, TN 37403 USA

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2017年 / 14卷 / 05期

关键词：

Boundary value problem; Caputo-Hadamard fractional derivative; implicit fractional differential equations; fractional integral; existence; stability; fixed point; impulses; HYBRID SYSTEMS;

D O I：

10.1007/s00009-017-1012-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the authors establish the existence and uniqueness of solutions for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and Caputo-Hadamard type fractional derivatives. The stability of this problem is also studied. The arguments are based on the Banach contraction principle and Schaefer's fixed point theorem. Two examples are presented to show the applicability of the results.

引用

页数：21

共 25 条

[1]

Abbas S., 2012, TOPICS FRACTIONAL DI, DOI 10.1007/978-1-4614-4036-9

[2]

[Anonymous], 2006, Contemporary Mathematics and its Applications

[3]

[Anonymous], 2015, Advanced Fractional Differential and Integral Equations

[4]

Bainov D.D, 1997, J APPL MATH STOCHAST, V10, P89

[5] Compositions of Hadamard-type fractional integration operators and the semigroup property [J].

Butzer, PL ;

Kilbas, AA ;

Trujillo, JJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 269 (02) :387-400

[6] Identification of switched linear systems using subspace and integer programming techniques [J].

Egbunonu, P. ;

Guay, M. .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2007, 1 (04) :577-592

[7]

Graef J. R., 2013, DEGRUYTER SERIES NON, V20

[8]

Granas A, 2003, Fixed point theory, DOI DOI 10.1007/978-0-387-21593-8

[9]

Hadamard J., 1892, J. Pure Appl. Math, V4, P101

[10] Caputo-type modification of the Hadamard fractional derivatives [J].

Jarad, Fahd ;

Abdeljawad, Thabet ;

Baleanu, Dumitru .

ADVANCES IN DIFFERENCE EQUATIONS, 2012,

← 1 2 3 →