Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer-Katugampola fractional derivative

被引：27
作者：
Ahmed, Idris [1 ,2 ,3 ]
Kumam, Poom [2 ,4 ]
Jarad, Fahd [5 ]
Borisut, Piyachat [1 ,2 ]
Sitthithakerngkiet, Kanokwan [6 ]
Ibrahim, Alhassan [7 ]
机构：
[1] King Mongkuts Univ Technol Thonburi KMUTT, Fac Sci, Dept Math, KMUTTFixed Point Res Lab, Room SCL 802 Fixed Point Lab,Sci Lab Bldg, Bangkok, Thailand
[2] King Mongkuts Univ Technol Thonburi KMUTT, Ctr Excellence Theoret & Computat Sci TaCS CoE, Sci Lab Bldg, Bangkok, Thailand
[3] Sule Lamido Univ, Dept Math & Comp Sci, Kafin Hausa, Nigeria
[4] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
[5] Cankaya Univ, Fac Arts & Sci, Dept Math, Ankara, Turkey
[6] King Mongkuts Univ Technol North Bangkok KMUTNB, Fac Appl Sci, Dept Math, Intelligent & Nonlinear Dynam Innovat Res Ctr, Bangkok, Thailand
[7] Bayero Univ Kano, Sch Continuing Educ, Kano, Nigeria
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期
关键词：
Hilfer fractional derivative; Stability; Volterra integral equation; Nonlocal integral condition; INITIAL-VALUE PROBLEMS; DIFFERENTIAL-EQUATIONS; EXISTENCE;
D O I：
10.1186/s13662-020-02681-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville-Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii's fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.
引用
收藏
页数：18
相关论文
共 54 条
[1]   Existence and Ulam stability for fractional differential equations of Hilfer-Hadamard type [J].
Abbas, S. ;
Benchohra, M. ;
Lagreg, J. E. ;
Alsaedi, A. ;
Zhou, Y. .
ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[2]  
Abbas S., 2019, MATHEMATICS-BASEL, V7
[3]   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
[4]   A semigroup-like Property for Discrete Mittag-Leffler Functions [J].
Abdeljawad, Thabet ;
Jarad, Fahd ;
Baleanu, Dumitru .
ADVANCES IN DIFFERENCE EQUATIONS, 2012, :1-7
[5]  
Abdo M.S., 2019, ARXIV190913680
[6]   Stability Results for Implicit Fractional Pantograph Differential Equations via φ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition [J].
Ahmed, Idris ;
Kumam, Poom ;
Shah, Kamal ;
Borisut, Piyachat ;
Sitthithakerngkiet, Kanokwan ;
Ahmed Demba, Musa .
MATHEMATICS, 2020, 8 (01)
[7]   Generalized Liouville-Caputo Fractional Differential Equations and Inclusions with Nonlocal Generalized Fractional Integral and Multipoint Boundary Conditions [J].
Alsaedi, Ahmed ;
Alghanmi, Madeaha ;
Ahmad, Bashir ;
Ntouyas, Sotiris K. .
SYMMETRY-BASEL, 2018, 10 (12)
[8]   Ulam Stability for Delay Fractional Differential Equations with a Generalized Caputo Derivative [J].
Ameen, Raad ;
Jarad, Fahd ;
Abdeljawad, Thabet .
FILOMAT, 2018, 32 (15) :5265-5274
[9]  
[Anonymous], 2009, BOUND VALUE PROBL, DOI DOI 10.1155/2009/708576
[10]  
[Anonymous], 2019, ADV DIFFER EQU-NY
123456