EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A NONLINEAR FRACTIONAL INITIAL VALUE PROBLEM INVOLVING CAPUTO DERIVATIVES

被引：19

作者：

Appell, Juergen ^{[1
]}

Lopez, Belen ^{[2
]}

Sadarangani, Kishin ^{[2
]}

机构：

[1] Univ Wurzburg, Math Inst, Campus Hubland Nord,Emil Fischer Str 30, D-97074 Wurzburg, Germany

[2] Univ Las Palmas Gran Canaria, Dept Matemat, Campus Tafira Baja, E-35017 Las Palmas De Gc, Spain

来源：

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS | 2018年 / 2卷 / 01期

关键词：

Initial value problem; Caputo derivative; Singular integral equation; Browder fixed point theorem; Matkowski fixed point theorem;

D O I：

10.23952/jnva.2.2018.1.03

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we give a sufficient condition for the existence and uniqueness interval of continuous solutions to a class of fractional initial value problems involving Caputo derivatives when the data functions satisfy a non-classical Lipschitz condition. The main tool used in the paper is a fixed point theorem for generalized contractions due to Browder-Matkowski.

引用

页码：25 / 33

页数：9

共 10 条

[1] Some generalizations of Darbo fixed point theorem and applications [J].

Aghajani, Asadollah ;

Banas, Jozef ;

Sabzali, Navid .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2013, 20 (02) :345-358

[2]

[Anonymous], 2006, THEORY APPL FRACTION

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4]

[Anonymous], 1968, NEDERL AKAD WETENS A, DOI DOI 10.1016/S1385-7258(68)50004-0

[5]

Ferreira R., 2016, ELECT J DIFFERENTIAL, V2016, P1

[6]

Kelley WG, 2010, UNIVERSITEXT, P1, DOI 10.1007/978-1-4419-5783-2

[7]

Matkowski J., 1982, FUNKC EKVACIOJ-SER I, V25, P127

[8]

Matkowski J., 1975, Dissertationes Mathematicae, V127, P1

[9]

Reich S., 2014, Developments in Mathematics, VVolume 34

[10]

Rus I.A., 2008, Fixed Point Theory

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