EXISTENCE AND STABILITY THEORY OF PANTOGRAPH CONFORMABLE FRACTIONAL DIFFERENTIAL PROBLEM

被引：15

作者：

Sher, Muhammad ^{[1
]}

Khan, Aziz ^{[2
]}

Shah, Kamal ^{[1
,2
]}

Abdeljawad, Thabet ^{[2
,3
]}

机构：

[1] Univ Malakand, Dept Math, Chakdara Dir L, Khyber Pakhtunk, Pakistan

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

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

来源：

THERMAL SCIENCE | 2023年 / 27卷 / Special Issue 1期

关键词：

conformable fractional derivative; EU of results; stability; Krasnoselskii's fixed point theorem;

D O I：

10.2298/TSCI23S1237S

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

The purpose of this paper is to investigate the existence and uniqueness (EU) of solutions to a class of conformable fractional differential equations (DE) with delay term using Krasnoselskii's fixed point theorem. The proposed problem is devoted to non-local initial value problems. Such problems are increasingly oc-curred in applications like in the filed of quantum mechanics and electrodynam-ics. The theoretical analysis is further enriched by establishing stability theory due to Ulam and its different kinds including "Ulam-Hyers (UH), generalized Ulam-Hyers (GUH), Ulam-Hyers-Rassias (UHR), and generalized Ulam-Hy-ers-Rassias (GUHR)" stability for the considered class. The obtain analysis is then testified by an example.

引用

页码：S237 / S244

页数：8

共 36 条

[1] On conformable fractional calculus [J].

Abdeljawad, Thabet .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 :57-66

[2] Ulam stability to a toppled systems of nonlinear implicit fractional order boundary value problem [J].

Ali, Zeeshan ;

Zada, Akbar ;

Shah, Kamal .

BOUNDARY VALUE PROBLEMS, 2018,

[3] On Ulam's Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations [J].

Ali, Zeeshan ;

Zada, Akbar ;

Shah, Kamal .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (05) :2681-2699

[4] Properties of the Katugampola fractional derivative with potential application in quantum mechanics [J].

Anderson, Douglas R. ;

Ulness, Darin J. .

JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (06)

[5]

[Anonymous], 1993, FRACTIONAL INTEGRALS, V1

[6] Nonlocal Cauchy problem for abstract fractional semilinear evolution equations [J].

Balachandran, K. ;

Park, J. Y. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (10) :4471-4475

[7] Krasnoselskii's fixed point theorem and stability [J].

Burton, TA ;

Furumochi, T .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 49 (04) :445-454

[8]

Diethelm K., 2010, LECT NOTES MATH, V204

[9] Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives [J].

Ekici, Mehmet ;

Mirzazadeh, Mohammad ;

Eslami, Mostafa ;

Zhou, Qin ;

Moshokoa, Seithuti P. ;

Biswas, Anjan ;

Belic, Milivoj .

OPTIK, 2016, 127 (22) :10659-10669

[10] Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations [J].

Eslami, Mostafa .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 285 :141-148

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