Existence results for abstract fractional differential equations with nonlocal conditions via resolvent operators

被引：40

作者：

Hernandez, Eduardo ^{[1
]}

O'Regan, Donal ^{[2
]}

Balachandran, Krishnan ^{[3
]}

机构：

[1] Univ Sao Paulo, Fac Filosofia Ciencias & Letras Ribeirao Preto, Dept Computacao & Matemat, BR-14049 Ribeirao Preto, SP, Brazil

[2] Natl Univ Ireland Galway, Dept Math, Galway, Ireland

[3] Bharathiar Univ, Dept Math, Coimbatore 641046, Tamil Nadu, India

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2013年 / 24卷 / 01期

关键词：

Fractional derivatives; Abstract Cauchy problem; Resolvent of linear operators; EVOLUTION-EQUATIONS; CAUCHY-PROBLEMS; MILD SOLUTION;

D O I：

10.1016/j.indag.2012.06.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In our paper [10] we discussed an error in the recent literature on abstract fractional differential equations and we proposed a different approach to treat these type of problems. By noting that the results by Hernandez et al. (2010) [10] are not applicable for problems with nonlocal conditions, in this paper we study the existence of mild solutions for a class of abstract fractional differential equations with nonlocal conditions. An application involving a partial differential equation with a fractional temporal derivative and nonlocal conditions is considered. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：68 / 82

页数：15

共 33 条

[1] A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative [J].

Agarwal, Ravi P. ;

Belmekki, Mohammed ;

Benchohra, Mouffak .

ADVANCES IN DIFFERENCE EQUATIONS, 2009, :1-47

[2]

[Anonymous], 2006, THEORY APPL FRACTION

[3]

[Anonymous], 1993, MONOGR MATH

[4]

[Anonymous], 1987, NONLINEAR OPERATORS

[5]

[Anonymous], 2009, NONLINEAR STUD

[6]

[Anonymous], 2010, INT J MATH ANAL

[7] Existence results for fractional order semilinear functional differential equations with nondense domain [J].

Belmekki, Mohammed ;

Benchohra, Mouffak .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (02) :925-932

[8] THEOREMS ABOUT THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF A SEMILINEAR EVOLUTION NONLOCAL CAUCHY-PROBLEM [J].

BYSZEWSKI, L .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 162 (02) :494-505

[9]

Byszewski L., 1991, Applicable Analysis, V40, P11

[10] Cauchy problem for fractional diffusion equations [J].

Eidelman, SD ;

Kochubei, AN .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 199 (02) :211-255

← 1 2 3 4 →