Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations

被引：39

作者：

Ali, Arshad ^{[1
]}

Shah, Kamal ^{[1
]}

Jarad, Fahd ^{[2
]}

Gupta, Vidushi ^{[3
]}

Abdeljawad, Thabet ^{[4
]}

机构：

[1] Univ Malakand, Dept Math, Khyber Pakhtunkhwa, Pakistan

[2] Cankaya Univ, Fac Arts & Sci, Dept Math, Ankara, Turkey

[3] Indian Inst Technol Guwahati, Dept Math, Gauhati, India

[4] Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 1期

关键词：

Coupled system; Arbitrary order differential equations; Impulsive conditions; Hyers-Ulam stability; HYERS-ULAM STABILITY; POSITIVE SOLUTIONS;

D O I：

10.1186/s13662-019-2047-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to obtain conditions for the existence and uniqueness of positive solutions. We discuss Hyers-Ulam (HU) type stability of the concerned solutions and provide an example for illustration of the obtained results.

引用

收藏

页数：21

相关论文

共 48 条

[1] On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives [J].

Abdeljawad, Thabet ;

Jarad, Fahd ;

Baleanu, Dumitru .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (10) :1775-1786

[2] On Riemann-Liouville fractional q-difference equations and their application to retarded logistic type model [J].

Abdeljawad, Thabet ;

Alzabut, Jehad .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (18) :8953-8962

[3] Discrete Mittag-Leffler kernel type fractional difference initial value problems and Gronwall's inequality [J].

Abdeljawad, Thabet ;

Al-Mdallal, Qasem M. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 339 :218-230

[4] A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel [J].

Abdeljawad, Thabet .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,

[5] A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems [J].

Abdeljawad, Thabet ;

Alzabut, Jehad ;

Baleanu, Dumitru .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,

[6] Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives [J].

Abdeljawad, Thabet ;

Baleanu, Dumitru ;

Jarad, Fahd .

JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (08)

[7] Fractional semilinear equations with causal operators [J].

Agarwal, Ravi P. ;

Asma ;

Lupulescu, Vasile ;

O'Regan, Donal .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2017, 111 (01) :257-269

[8] Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions [J].

Ahmad, Bashir ;

Nieto, Juan J. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) :1838-1843

[9]

Ali A., 2019, ADV DIFFER EQU, V2019

[10] On Ulam's Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations [J].

Ali, Zeeshan ;

Zada, Akbar ;

Shah, Kamal .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (05) :2681-2699

← 1 2 3 4 5 →