Ulam-Hyers-Rassias stability for generalized fractional differential equations

被引：9

作者：

Boucenna, Djalal ^{[1
]}

Ben Makhlouf, Abdellatif ^{[2
,3
]}

El-hady, El-sayed ^{[2
,4
]}

Hammami, Mohamed Ali ^{[3
]}

机构：

[1] High Sch Technol Teaching, Enset, Skikda, Algeria

[2] Jouf Univ, Coll Sci, Math Dept, POB 2014, Sakaka, Saudi Arabia

[3] Univ Sfax, Fac Sci Sfax, Dept Math, Sfax, Tunisia

[4] Suez Canal Univ, Fac Comp & Informat, Basic Sci Dept, Ismailia, Egypt

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 13期

关键词：

nonlinear fractional differential equations; Ulam– Hyers– Rassias stability; generalized fractional derivative; FIXED-POINT APPROACH; FUNCTIONAL-EQUATIONS; PART;

D O I：

10.1002/mma.7406

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a generalized Gronwall inequality with singularity. Using this inequality, we investigate the existence, uniqueness, and Ulam-Hyers-Rassias stability for solutions of a class of generalized nonlinear fractional differential equations of order alpha (1 < alpha < 2). In this way, we improve and generalize several earlier outcomes.

引用

页码：10267 / 10280

页数：14

共 41 条

[1] Fractional Differential Equations With Dependence on the Caputo-Katugampola Derivative [J].

Almeida, Ricardo ;

Malinowska, Agnieszka B. ;

Odzijewicz, Tatiana .

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2016, 11 (06)

[2]

[Anonymous], 2012, ABSTRACT APPL ANAL, DOI [10.1155/2012/716936, DOI 10.1155/2012/716936]

[3]

Aoki T., 1950, J MATH SOC JAPAN, V2, P64, DOI DOI 10.2969/JMSJ/00210064

[4] THE STABILITY OF CERTAIN FUNCTIONAL-EQUATIONS [J].

BAKER, JA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 112 (03) :729-732

[5] Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations [J].

Baleanu, Dumitru ;

Wu, Guo-Cheng ;

Zeng, Sheng-Da .

CHAOS SOLITONS & FRACTALS, 2017, 102 :99-105

[6] Existence and Stability Results for Generalized Fractional Differential Equations [J].

Ben Makhlouf, A. ;

Boucenna, D. ;

Hammami, M. A. .

ACTA MATHEMATICA SCIENTIA, 2020, 40 (01) :141-154

[7] Finite-Time Stability of Linear Caputo-Katugampola Fractional-Order Time Delay Systems [J].

Ben Makhlouf, Abdellatif ;

Nagy, A. M. .

ASIAN JOURNAL OF CONTROL, 2020, 22 (01) :297-306

[8]

Ben Makhlouf A, 2018, MATH COMMUN, V23, P119

[9]

Boroomand A, 2009, LECT NOTES COMPUT SC, V5506, P883, DOI 10.1007/978-3-642-02490-0_108

[10] LINEARIZED STABILITY ANALYSIS OF CAPUTO-KATUGAMPOLA FRACTIONAL-ORDER NONLINEAR SYSTEMS [J].

Boucenna, D. ;

Ben Makhlouf, A. ;

Naifar, O. ;

Guezane-Lakoud, A. ;

Hammami, M. A. .

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2018, 2018

← 1 2 3 4 5 →