Ulam-Hyers stability of pantograph fractional stochastic differential equations

被引：16

作者：

Mchiri, Lassaad ^{[1
]}

Ben Makhlouf, Abdellatif ^{[2
]}

Rguigui, Hafedh ^{[3
]}

机构：

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

[2] Jouf Univ, Coll Sci, Dept Math, Aljouf, Saudi Arabia

[3] Umm Al Qura Univ, Al Qunfudhah Univ Coll, Dept Math, Al Qunfudhah, Saudi Arabia

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 04期

关键词：

Caputo derivative; Ulam stability; POLYNOMIAL STABILITY; EXISTENCE; DYNAMICS;

D O I：

10.1002/mma.8745

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence and uniqueness theorem (EUT) of Pantograph fractional stochastic differential equations (PFSDE) using the Banach fixed point theorem (BFPT). We show the Ulam-Hyers stability (UHS) of PFSDE by the generalized Gronwall inequalities (GGI). We illustrate our results by two examples.

引用

页码：4134 / 4144

页数：11

共 37 条

[1] A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability [J].

Abbas, Said ;

Benchohra, Mouffak ;

Lazreg, Jamal-Eddine ;

Zhou, Yong .

CHAOS SOLITONS & FRACTALS, 2017, 102 :47-71

[2] A Generalized Definition of the Fractional Derivative with Applications [J].

Abu-Shady, M. ;

Kaabar, Mohammed K. A. .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2021, 2021

[3] Dynamics of the worm transmission in wireless sensor network in the framework of fractional derivatives [J].

Achar, Sindhu J. ;

Baishya, Chandrali ;

Kaabar, Mohammed K. A. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (08) :4278-4294

[4]

Ahmad B., 2017, Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

[5] Ulam-Hyers stability of Caputo type fractional stochastic neutral differential equations [J].

Ahmadova, Arzu ;

Mahmudov, Nazim, I .

STATISTICS & PROBABILITY LETTERS, 2021, 168

[6] Caputo-Hadamard Fractional Derivatives of Variable Order [J].

Almeida, Ricardo .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (01) :1-19

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

Anguraj, A. ;

Vinodkumar, A. ;

Malar, K. .

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

[8] On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations [J].

Appleby, John A. D. ;

Patterson, Denis D. .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2016, (63)

[9]

Baker C. T. H., 2000, Electronic Transactions on Numerical Analysis, V11

[10]

Baleanu D., 2011, Fractional Dynamics and Control, DOI [10.1007/978-1-4614-0457-6, DOI 10.1007/978-1-4614-0457-6]

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