NEW FIXED POINT THEOREMS FOR SUM OPERATORS IN THE SET Ph,e AND THEIR APPLICATIONS TO NONLINEAR FRACTIONAL DIFFERENTIAL PROBLEMS

被引：1

作者：

Zhang, Lingling ^{[1
]}

Tian, Huimin ^{[1
]}

机构：

[1] Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Shanxi, Peoples R China

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2022年 / 59卷 / 2B期

关键词：

  Mixed monotone operator; existence and uniqueness; fractional differential equations; MIXED MONOTONE-OPERATORS; POSITIVE SOLUTIONS; EXISTENCE; UNIQUENESS; EQUATION;

D O I：

10.12775/TMNA.2021.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper presents several new fixed point theorems for some sum operators. Without any compactness or continuity assumptions, we establish sufficient conditions for some operators to have unique fixed points and describe sequences converging to the fixed points. The main results are obtained by the cone theory and monotone iterative technique. Besides, as applications, these new fixed point theorems are used to study the existence and uniqueness of solutions for a class of nonlinear fractional differential equations.

引用

页码：719 / 735

页数：17

共 23 条

[1] Positive solutions for boundary value problem of nonlinear fractional differential equation [J].

Bai, ZB ;

Lü, HS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) :495-505

[2]

Baleanu D., 2011, Fractional Dynamics and Control, DOI [10.1007/978-1-4614-0457-6, DOI 10.1007/978-1-4614-0457-6]

[3]

Deimling K., 2010, Nonlinear Functional Analysis

[4] Existence of a positive solution to systems of differential equations of fractional order [J].

Goodrich, Christopher S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) :1251-1268

[5] Existence of a positive solution to a class of fractional differential equations [J].

Goodrich, Christopher S. .

APPLIED MATHEMATICS LETTERS, 2010, 23 (09) :1050-1055

[6] COUPLED FIXED-POINTS OF NONLINEAR OPERATORS WITH APPLICATIONS [J].

GUO, D ;

LAKSHMIKANTHAM, V .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (05) :623-632

[7] Fixed point theorems for mixed monotone operators and applications to integral equations [J].

Harjani, J. ;

Lopez, B. ;

Sadarangani, K. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (05) :1749-1760

[8]

Hilfer R., 2000, APPL FRACTIONAL CALC, pp 472, DOI [10.1142/3779, DOI 10.1142/3779]

[9] Existence of positive solutions to an arbitrary order fractional differential equation via a mixed monotone operator method [J].

Jleli, Mohamed ;

Samet, Bessem .

NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2015, 20 (03) :367-376

[10]

Kilbas A.A., 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0

← 1 2 3 →