BLOW-UP PHENOMENA PROFILE FOR HADAMARD FRACTIONAL DIFFERENTIAL SYSTEMS IN FINITE TIME

被引：10

作者：

Ma, Li ^{[1
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230601, Anhui, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2019年 / 27卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Hadamard Fractional Derivative; Lower and Upper Solutions Method; Weak Singularity; Blow-Up Solution; NUMERICAL-SOLUTIONS; EQUATIONS;

D O I：

10.1142/S0218348X19500932

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this paper is to investigate the weak singularity of solutions for some nonlinear Hadamard fractional differential systems (HFDSs). By constructing proper Banach space and employing lower and upper solutions technique, we prove the existence of the blow-up solutions for a class of HFDSs. In addition, we establish a more general condition than the classical Lipschitz condition which is employed to guarantee the equivalence between the solutions to HFDS and the corresponding functional operator. Also several examples are presented to verify our theoretical results.

引用

页数：10

共 40 条

[1] Ahmad B., 2017, Hadamard-type fractional differential equations, inclusions and inequalities
[2] [Anonymous], 1992, NONLINEAR PARABOLIC, DOI DOI 10.1007/978-1-4615-3034-3
[3] [Anonymous], 2012, FRACTIONAL DYNAMICS
[4] [Anonymous], 2014, MITTAG LEFFLER FUNCT
[5] Almost automorphic mild solutions to fractional differential equations
Araya, Daniela
Lizama, Carlos
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (11) : 3692 - 3705
[6] Hopf bifurcation for a class of fractional differential equations with delay
Babakhani, Azizollah
Baleanu, Dumitru
Khanbabaie, Reza
[J]. NONLINEAR DYNAMICS, 2012, 69 (03) : 721 - 729
[7] On the existence of blow up solutions for a class of fractional differential equations
Bai, Zhanbing
Chen, YangQuan
Lian, Hairong
Sun, Sujing
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2014, 17 (04) : 1175 - 1187
[8] New aspects of poor nutrition in the life cycle within the fractional calculus
Baleanu, Dumitru
Jajarmi, Amin
Bonyah, Ebenezer
Hajipour, Mojtaba
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[9] About the kinetic description of fractional diffusion equations modeling chemotaxis
Bellouquid, Abdel
Nieto, Juanjo
Urrutia, Luis
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2016, 26 (02) : 249 - 268
[10] On monotone iterative methods for a nonlinear singularly perturbed reaction-diffusion problem
Boglaev, I
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 162 (02) : 445 - 466

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