Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations

被引：9

作者：

Ali, Sajjad ^{[1
]}

Abdeljawad, Thabet ^{[2
]}

Shah, Kamal ^{[3
]}

Jarad, Fahd ^{[4
]}

Arif, Muhammad ^{[1
]}

机构：

[1] Abdul Wali Khan Univ, Dept Math, Mardan, Khyber Pakhtunk, Pakistan

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

[3] Univ Malakand, Dept Math, Khyber Pakhtunkhwa, Pakistan

[4] Cankaya Univ, Dept Math, Ankara, Turkey

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 1期

关键词：

Monotone iterative technique; Fractional differential equations; Extremal solutions; Ulam stability; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS; EXISTENCE;

D O I：

10.1186/s13662-019-2151-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative technique. With the help of the proposed procedure, the convergence criteria for extremal solutions are smoothly achieved. Furthermore, a major aspect is devoted to the investigation of Ulam-Hyers type stability analysis which is also established. For the verification of our work, we provide some suitable examples along with their graphical represntation and errors estimates.

引用

页数：19

共 45 条

[1] On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives [J].

Abdeljawad, Thabet ;

Jarad, Fahd ;

Baleanu, Dumitru .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (10) :1775-1786

[2] Fractional logistic models in the frame of fractional operators generated by conformable derivatives [J].

Abdeljawad, Thabet ;

Al-Mdallal, Qasem M. ;

Jarad, Fahd .

CHAOS SOLITONS & FRACTALS, 2019, 119 (94-101) :94-101

[3] Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives [J].

Abdeljawad, Thabet ;

Baleanu, Dumitru ;

Jarad, Fahd .

JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (08)

[4]

Adjabi Y, 2016, J COMPUT ANAL APPL, V21, P661

[5] 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

[6] Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions [J].

Ahmad, Bashir ;

Nieto, Juan J. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) :1838-1843

[7] Monotone iterative sequences for nonlinear boundary value problems of fractional order [J].

Al-Refai, Mohammed ;

Hajji, Mohamed Ali .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) :3531-3539

[8] Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations [J].

Ali, Arshad ;

Shah, Kamal ;

Jarad, Fahd ;

Gupta, Vidushi ;

Abdeljawad, Thabet .

ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)

[9] 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

[10] Ulam Stability for Delay Fractional Differential Equations with a Generalized Caputo Derivative [J].

Ameen, Raad ;

Jarad, Fahd ;

Abdeljawad, Thabet .

FILOMAT, 2018, 32 (15) :5265-5274

← 1 2 3 4 5 →