Existence of Monotone Positive Solutions for Caputo-Hadamard Nonlinear Fractional Differential Equation with Infinite-Point Boundary Value Conditions

被引：7

作者：

Guo, Limin ^{[1
]}

Li, Cheng ^{[1
]}

Zhao, Jingbo ^{[1
]}

机构：

[1] Changzhou Inst Technol, Sch Automot Engn, Changzhou 213002, Peoples R China

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Caputo-Hadamard fractional differential equation; iterative positive solution; infinite-point; sum operator; P-LAPLACIAN; SYSTEM; SINGULARITIES; UNIQUENESS; OPERATORS; THEOREMS;

D O I：

10.3390/sym15050970

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Numerical solutions and approximate solutions of fractional differential equations have been studied by mathematicians recently and approximate solutions and exact solutions of fractional differential equations are obtained in many kinds of ways, such as Lie symmetry, variational method, the optimal ADM method, and so on. In this paper, we obtain the positive solutions by iterative methods for sum operators. Green's function and the properties of Green's function are deduced, then based on the properties of Green's function, the existence of iterative positive solutions for a nonlinear Caputo-Hadamard infinite-point fractional differential equation are obtained by iterative methods for sum operators; an example is proved to illustrate the main result.

引用

页数：14

共 44 条

[1] Topological degree theory and Caputo-Hadamard fractional boundary value problems [J].

Amara, Abdelkader ;

Etemad, Sina ;

Rezapour, Shahram .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

[2]

Ardjouni A., 2019, OPEN J MATH ANAL, V3, P62, DOI [10.30538/psrp-oma2019.0033, DOI 10.30538/PSRP-OMA2019.0033]

[3] Existence and multiplicity of solutions for fractional p(x, .)-Kirchhoff-type problems in RN [J].

Azroul, E. ;

Benkirane, A. ;

Shimi, M. .

APPLICABLE ANALYSIS, 2021, 100 (09) :2029-2048

[4] Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation [J].

Bakhshandeh-Chamazkoti, Rohollah ;

Alipour, Mohsen .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2022, 200 :97-107

[5] Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control [J].

Bhalekar, Sachin ;

Daftardar-Gejji, Varsha .

INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 2011

[6] Neural network Script capital L1 adaptive control for a class of uncertain fractional order nonlinear systems [J].

Boulham, Ihab Abderraouf ;

Boubakir, Ahsene ;

Labiod, Salim .

INTEGRATION-THE VLSI JOURNAL, 2022, 83 :1-11

[7] BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATION WITH HADAMARD FRACTIONAL INTEGRAL AND ANTI-PERIODIC CONDITIONS [J].

Boutiara, Abdelatif ;

Benbachir, Maamar ;

Guerbati, Kaddour .

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2021, 36 (04) :735-748

[8] Nonlinear fractional differential equations with integral boundary value conditions [J].

Cabada, Alberto ;

Hamdi, Zakaria .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 228 :251-257

[9] Maximum principles for the fractional p-Laplacian and symmetry of solutions [J].

Chen, Wenxiong ;

Li, Congming .

ADVANCES IN MATHEMATICS, 2018, 335 :735-758

[10] Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions [J].

Chen, Wenxiong ;

Li, Congming ;

Li, Guanfeng .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (02)

← 1 2 3 4 5 →