Solvability and stability analysis of a coupled system involving generalized fractional derivatives

被引：7

作者：

Djaout, Abdallah ^{[1
]}

Benbachir, Maamar ^{[2
]}

Lakrib, Mustapha ^{[3
]}

Matar, Mohammed M. ^{[4
]}

Khan, Aziz ^{[5
]}

Abdeljawad, Thabet ^{[5
,6
,7
]}

机构：

[1] Saad Dahlab Univ, Fac Sci, Blida, Algeria

[2] Natl Higher Sch Math, Algiers, Algeria

[3] Univ Djillali Liabes Sidi Bel Abbes, Lab Math, Sidi Bel Abbes, Algeria

[4] Al Azhar Univ Gaza, Dept Math, Gaza, Palestine

[5] Prince Sultan Univ, Dept Math & Sci, POB 66833, Riyadh 11586, Saudi Arabia

[6] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

[7] Kyung Hee Univ, Dept Math, 26 Kyungheedae Ro, Seoul 02447, South Korea

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 04期

关键词：

existence and uniqueness; generalized fractional derivative and integral; boundary value problem; minimal and maximal solutions; Ulam-Hyers; DIFFERENTIAL-EQUATIONS; POSITIVE SOLUTIONS; EXISTENCE; UNIQUENESS;

D O I：

10.3934/math.2023393

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we investigate the existence of unique maximal and minimal solutions for a coupled differential system in terms of generalized fractional derivative with arbitrary order. The iterative technique of a fixed point operator together with the properties of green's function are used basically. Moreover, we investigate the generalized Ulam-Hyers stability of the solution for the given coupled system. Finally, some examples are given to illustrate the theoretic results.

引用

收藏

页码：7817 / 7839

页数：23

相关论文

共 26 条

[1] Conformable fractional polytropic gas spheres [J].

Abdel-Salam, Emad. A. -B. ;

Nouh, Mohamed I. .

NEW ASTRONOMY, 2020, 76

[2] Geometrical study and solutions for family of burgers-like equation with fractional order space time [J].

Abdel-Salam, Emad A-B ;

Jazmati, Mohamed S. ;

Ahmad, Hijaz .

ALEXANDRIA ENGINEERING JOURNAL, 2022, 61 (01) :511-521

[3] Fractional derivative order analysis and temperature-dependent properties on p- and SV-waves reflection under initial stress and three-phase-lag model [J].

Abo-Dahab, S. M. ;

Kilany, A. A. ;

Abdel-Salam, Emad A-B ;

Hatem, A. .

RESULTS IN PHYSICS, 2020, 18

[4] Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations [J].

Ali, Sajjad ;

Abdeljawad, Thabet ;

Shah, Kamal ;

Jarad, Fahd ;

Arif, Muhammad .

ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)

[5] On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations [J].

Ali, Sajjad ;

Shah, Kamal ;

Jarad, Fahd .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (03) :969-981

[6]

[Anonymous], 1990, Nonlinear Functional Analysis and its Applications

[7] ARTIFICIAL NEURAL NETWORK MODELING OF THE CONFORMABLE FRACTIONAL ISOTHERMAL GAS SPHERES [J].

Azzam, Yosry. A. ;

Abdel-Salam, Emad A. -B. ;

Nouh, Mohamed I. .

REVISTA MEXICANA DE ASTRONOMIA Y ASTROFISICA, 2021, 57 (01) :189-198

[8] Positive solutions of nonlinear fractional differential equations with integral boundary value conditions [J].

Cabada, Alberto ;

Wang, Guotao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (01) :403-411

[9] Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model [J].

Elhag, S. H. ;

Bayones, Fatimah S. ;

Kilany, A. A. ;

Abo-Dahab, S. M. ;

Abdel-Salam, Emad A-B ;

Elsagheer, M. ;

Abd-Alla, A. M. .

ADVANCES IN MATHEMATICAL PHYSICS, 2022, 2022

[10] New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions [J].

Feng, Meiqiang ;

Zhang, Xuemei ;

Ge, WeiGao .

BOUNDARY VALUE PROBLEMS, 2011,