Study of multi term delay fractional order impulsive differential equation using fixed point approach

被引：4

作者：

Ali, Amjad ^{[1
]}

Shah, Kamal ^{[2
,3
]}

Ahmad, Dildar ^{[1
]}

Rahman, Ghaus Ur ^{[1
]}

Mlaiki, Nabil ^{[2
]}

Abdeljawad, Thabet ^{[2
,4
]}

机构：

[1] Univ Swat, Dept Math & Stat, Khyber Pakhtunkhwa, Pakistan

[2] Prince Sultan Univ, Dept Math & Sci, Riyadh 11585, Saudi Arabia

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

[4] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 07期

关键词：

impulsive delay differential equations; existence theory; Banach theorem; stability analysis; STABILITY;

D O I：

10.3934/math.2022644

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example.

引用

页码：11551 / 11580

页数：30

共 36 条

[1] On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives [J].

Abdeljawad, Thabet ;

Madjidi, Fadila ;

Jarad, Fahd ;

Sene, Ndolane .

MATHEMATICS, 2019, 7 (10)

[2] Existence results for a coupled system of nonlinear multi-term fractional differential equations with anti-periodic type coupled nonlocal boundary conditions [J].

Ahmad, Bashir ;

Alblewi, Manal ;

Ntouyas, Sotiris K. ;

Alsaedi, Ahmed .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (11) :8739-8758

[3] On an impulsive hybrid system of conformable fractional differential equations with boundary conditions [J].

Ahmad, Bashir ;

Alghanmi, Madeaha ;

Alsaedi, Ahmed ;

Agarwal, Ravi P. .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2020, 51 (05) :958-970

[4]

Ali A, 2019, FRONTIERS FUNCTIONAL, P73, DOI DOI 10.1007/978-3-030-28950-8

[5]

Ali A, 2016, J COMPUT THEOR NANOS, V13, P143, DOI [10.1166/jctn.2016.4781, 10.1166/jctn.2016.4781, DOI 10.1166/JCTN.2016.4781]

[6] Existence and stability of solution to a toppled systems of differential equations of non-integer order [J].

Ali, Amjad ;

Samet, Bessem ;

Shah, Kamal ;

Khan, Rahmat Ali .

BOUNDARY VALUE PROBLEMS, 2017,

[7]

Ali G, 2020, Arab Journal of Basic and Applied Sciences, V27, P471, DOI [10.1080/25765299.2020.1850621, 10.1080/25765299.2020.1850621, DOI 10.1080/25765299.2020.1850621]

[8] EXISTENCE OF SOLUTIONS OF NONLINEAR FRACTIONAL PANTOGRAPH EQUATIONS [J].

Balachandran, K. ;

Kiruthika, S. ;

Trujillo, J. J. .

ACTA MATHEMATICA SCIENTIA, 2013, 33 (03) :712-720

[9] A novel modeling of boundary value problems on the glucose graph [J].

Baleanu, Dumitru ;

Etemad, Sina ;

Mohammadi, Hakimeh ;

Rezapour, Shahram .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 100 (100)

[10]

Bellman R., 2008, Stability theory of differential equations

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