Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations

被引：40

作者：

Bedi, Pallavi ^{[1
]}

Kumar, Anoop ^{[1
]}

Abdeljawad, Thabet ^{[2
,3
,4
]}

Khan, Aziz ^{[2
]}

机构：

[1] Cent Univ Punjab, Dept Math & Stat, Bathinda, Punjab, India

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

[3] China Med Univ, Dept Med Res, Taichung, Taiwan

[4] Asia Univ, Dept Comp Sci & Informat Engn, Taichung, Taiwan

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Hilfer fractional derivative; Noninstantaneous impulsive conditions; Hausdorff measure of noncompactness; Resolvent operator functions; DIFFERENTIAL-EQUATIONS; OPERATORS;

D O I：

10.1186/s13662-020-02615-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence of mild solutions for neutral Hilfer fractional evolution equations with noninstantaneous impulsive conditions in a Banach space. We obtain the existence results by applying the theory of resolvent operator functions, Hausdorff measure of noncompactness, and Sadovskii's fixed point theorem. We also present an example to show the validity of obtained results.

引用

页数：16

共 39 条

[1] Fractional logistic models in the frame of fractional operators generated by conformable derivatives [J].

Abdeljawad, Thabet ;

Al-Mdallal, Qasem M. ;

Jarad, Fahd .

CHAOS SOLITONS & FRACTALS, 2019, 119 (94-101) :94-101

[2]

[Anonymous], 2018, Int J Pure Appl Math

[3] Numerical approximation of Riemann-Liouville definition of fractional derivative: From Riemann-Liouville to Atangana-Baleanu [J].

Atangana, Abdon ;

Gomez-Aguilar, J. F. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (05) :1502-1523

[4] Measures of noncompactness in the study of solutions of nonlinear differential and integral equations [J].

Banas, Jozef .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2012, 10 (06) :2003-2011

[5] Nonlinear generalized fractional differential equations with generalized fractional integral conditions [J].

Belmor, Samiha ;

Ravichandran, Chokkalingam ;

Jarad, Fahd .

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2020, 14 (01) :114-123

[6] Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces [J].

Chalishajar, Dimplekumar ;

Ravichandran, Chokkalingam ;

Dhanalakshmi, Shanmugam ;

Murugesu, Rangasamy .

APPLIED SYSTEM INNOVATION, 2019, 2 (02) :1-17

[7] On fractional resolvent operator functions [J].

Chen, Chuang ;

Li, Miao .

SEMIGROUP FORUM, 2010, 80 (01) :121-142

[8]

Chen P., 2016, ELECTRON J DIFFER EQ, V2016, DOI [10.1186/s13662-016-0969-1, DOI 10.1186/S13662-016-0969-1]

[9]

Daher SJ., 1978, NONLINEAR ANAL TMA, V2, P643, DOI [10.1016/0362-546X(78)90012-3, DOI 10.1016/0362-546X(78)90012-3]

[10] Existence of solutions for neutral integro-differential equations with state-dependent delay [J].

Fu, Xianlong ;

Huang, Rong .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 :743-759

← 1 2 3 4 →