Stability Results for Implicit Fractional Pantograph Differential Equations via φ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

被引：54

作者：

Ahmed, Idris ^{[1
,2
,3
]}

Kumam, Poom ^{[2
,4
]}

Shah, Kamal ^{[5
,6
]}

Borisut, Piyachat ^{[1
,2
]}

Sitthithakerngkiet, Kanokwan ^{[2
,7
]}

Ahmed Demba, Musa ^{[1
,2
,8
]}

机构：

[1] KMUTT, Fac Sci, Dept Math, Fixed Point Lab,KMUTTFixed Point Res Lab, Room SCL 802,126 Pracha Uthit Rd, Bangkok 10140, Thailand

[2] KMUTT, Ctr Excellence Theoret & Computat Sci TaCS CoE, 126 Pracha Uthit Rd,Sci Lab Bldg, Bangkok 10140, Thailand

[3] Sule Lamido Univ, Dept Math & Comp Sci, PMB 048, Kafin Hausa, Jigawa State, Nigeria

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

[5] Univ Malakand Chakadara DirL, Dept Math, Khyber Pakhtunkhwa 18800, Pakistan

[6] Prince Sultan Univ, Dept Math & Basic Sci, Riyadh 11586, Saudi Arabia

[7] KMUTNB, Fac Sci Appl, Dept Math, Intelligent & Nonlinear Dynam Innovat Res Ctr, Bangkok 10800, Thailand

[8] Kano Univ Sci & Technol, Fac Comp & Math Sci, Dept Math, Wudil 3244, Kano State, Nigeria

来源：

MATHEMATICS | 2020年 / 8卷 / 01期

关键词：

Hilfer fractional derivative; Ulam stability; pantograph differential equation; nonlocal integral condition; EXISTENCE; OPERATORS; CALCULUS;

D O I：

10.3390/math8010094

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer's and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

引用

页数：21

共 62 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]

Abdo M.S., 2019, ARXIV190913680

[3] Fractional Integro-Differential Equations Involving ψ-Hilfer Fractional Derivative [J].

Abdo, Mohammed S. ;

Panchal, Satish K. .

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2019, 11 (02) :338-359

[4]

Ahmad B., 2008, Communications in Applied Analysis, V12, P107

[5] Existence of solutions for impulsive integral boundary value problems of fractional order [J].

Ahmad, Bashir ;

Sivasundaram, S. .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2010, 4 (01) :134-141

[6] Impulsive Hilfer fractional differential equations [J].

Ahmed, Hamdy M. ;

El-Borai, Mahmoud M. ;

El-Owaidy, Hassan M. ;

Ghanem, Ahmed S. .

ADVANCES IN DIFFERENCE EQUATIONS, 2018,

[7]

Ali K.B., 2016, ELECTRON J DIFFER EQ, V2016, P1, DOI DOI 10.1186/S13662-016-0808-4

[8] A Caputo fractional derivative of a function with respect to another function [J].

Almeida, Ricardo .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 44 :460-481

[9] Existence and Stability Results for Random Impulsive Fractional Pantograph Equations [J].

Anguraj, A. ;

Vinodkumar, A. ;

Malar, K. .

FILOMAT, 2016, 30 (14) :3839-3854

[10]

[Anonymous], 2009, BOUND VALUE PROBL, DOI DOI 10.1155/2009/708576

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