Existence and Ulam stability results for two orders neutral fractional differential equations

被引：1

作者：

Khochemane, Houssem Eddine ^{[1
]}

Ardjouni, Abdelouaheb ^{[2
]}

Zitouni, Salah ^{[2
]}

机构：

[1] Ecole Normale Super Enseignement Technol, Azzaba, Skikda, Algeria

[2] Univ Souk Ahras, Dept Math & Informat, Souk Ahras 41000, Algeria

来源：

AFRIKA MATEMATIKA | 2022年 / 33卷 / 02期

关键词：

Fixed point theorems; Neutral fractional differential equations; Ulam stability; Caputo fractional derivative; BOUNDARY-VALUE-PROBLEMS;

D O I：

10.1007/s13370-022-00970-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence and uniqueness of mild solutions for a nonlinear neutral fractional differential equation with two orders of Caputo's fractional derivative using the Krasnoselskii and Banach fixed point theorems. We establish four types of Ulam stability: Ulam-Hyers, Ulam-Hyers-Rassias, generalized Ulam-Hyers and generalized Ulam-Hyers-Rassias. Two examples are given to substantiate the usefulness of the obtained results.

引用

页数：16

共 32 条

[1]

Abdo M.S., 2018, INT J MATH APPL, V6, P403

[2] A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions [J].

Agarwal, Ravi P. ;

Benchohra, Mouffak ;

Hamani, Samira .

ACTA APPLICANDAE MATHEMATICAE, 2010, 109 (03) :973-1033

[3] Existence of Solutions for Fractional Differential Inclusions with Antiperiodic Boundary Conditions [J].

Ahmad, Bashir ;

Otero-Espinar, Victoria .

BOUNDARY VALUE PROBLEMS, 2009,

[4] Stability analysis for a nonlinear coupled system of fractional hybrid delay differential equations [J].

Ahmad, Israr ;

Shah, Kamal ;

Rahman, Ghaus Ur ;

Baleanu, Dumitru .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (15) :8669-8682

[5] Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions [J].

Ali, Arshad ;

Shah, Kamal ;

Abdeljawad, Thabet ;

Mahariq, Ibrahim ;

Rashdan, Mostafa .

BOUNDARY VALUE PROBLEMS, 2021, 2021 (01)

[6] Study of implicit delay fractional differential equations under anti-periodic boundary conditions [J].

Ali, Arshad ;

Shah, Kamal ;

Abdeljawad, Thabet .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

[7]

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

[8] A computational algorithm for the numerical solution of fractional order delay differential equations [J].

Amin, Rohul ;

Shah, Kamal ;

Asif, Muhammad ;

Khan, Imran .

APPLIED MATHEMATICS AND COMPUTATION, 2021, 402

[9]

Anastassiou GA, 2011, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-1-4614-0703-4

[10]

[Anonymous], 2002, APPL ANAL

← 1 2 3 4 →