A Numerical Iterative Scheme for Solving Nonlinear Boundary Value Problems of Fractional Order 0 < α < 1

被引：0

作者：

Anwar, Muhammad Adnan ^{[1
]}

Rehman, Shafiq Ur ^{[1
]}

Ahmad, Fayyaz ^{[2
,3
]}

Qadir, Muhammad Irfan ^{[1
]}

机构：

[1] Univ Engn & Technol, Dept Math, Lahore, Pakistan

[2] Univ Politecn Cataluna, Dept Fis & Engn Nucl, Eduard Maristany 10, Barcelona 08019, Spain

[3] Univ Insubria, Dipartimento Sci & Alta Tecnol, Via Valleggio 11, I-22100 Como, Italy

来源：

PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS | 2019年 / 51卷 / 01期

关键词：

Fractional differential equation; boundary value problem; central difference scheme; Simpson's rule; iterative scheme; POSITIVE SOLUTIONS; EQUATIONS; DYNAMICS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Accurate numerical approximations for solving non linear fractional order boundary value problems are presented in this paper. To accomplish this goal, first- and second-order derivatives involved in the developed scheme are approximated by central finite difference scheme of order four. Whereas, integrals in this work are approximated by the composite Simpson's rule in the Caputo's definition. The performance of the proposed iterative scheme is demonstrated by solving nonlinear fractional order boundary value problems of order 0 < alpha < 1.

引用

页码：115 / 126

页数：12

共 50 条

[1] THE CONTROLLER DESIGN FOR SINGULAR FRACTIONAL-ORDER SYSTEMS WITH FRACTIONAL ORDER 0 < α < 1
Zhan, T.
Ma, S. P.
ANZIAM JOURNAL, 2018, 60 (02): : 230 - 248
[2] An iterative scheme for solving nonlinear two point boundary value problems
Qu, RB
Agarwal, RP
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1997, 64 (3-4) : 285 - 302
[3] Robust stabilization of uncertain descriptor fractional-order systems with the fractional order α(0 < α < 1)
Zhang, Xuefeng
Li, Bingxin
PROCEEDINGS OF THE 28TH CHINESE CONTROL AND DECISION CONFERENCE (2016 CCDC), 2016, : 560 - 563
[4] Monotone iterative sequences for nonlinear boundary value problems of fractional order
Al-Refai, Mohammed
Hajji, Mohamed Ali
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) : 3531 - 3539
[5] AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER 0 < α < 1
Xu, Wenjing
Xu, Wei
Lu, Kai
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2020, 23 (03) : 908 - 919
[6] Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order α: The 0 < α < 1 Case
Lu, Jun-Guo
Chen, Yang-Quan
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (01) : 152 - 158
[7] Robust stabilization for rectangular descriptor fractional order interval systems with order 0 < α < 1
Zhang, Xuefeng
Zhao, Zeli
APPLIED MATHEMATICS AND COMPUTATION, 2020, 366
[8] Comments on "Robust Stability and Stabilization of Fractional-Order Interval Systems With the Fractional Order α: The 0 < α < 1 Case"
Aguiar, Braulio
Gonzalez, Temoatzin
Bernal, Miguel
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2015, 60 (02) : 582 - 583
[9] Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: The 0 < α < 1 case
Zhang, Xuefeng
Chen, YangQuan
ISA TRANSACTIONS, 2018, 82 : 42 - 50
[10] Robust H∞ control for fractional order singular systems 0 < α < 1 with uncertainty
Li, Bingxin
Zhao, Xin
OPTIMAL CONTROL APPLICATIONS & METHODS, 2023, 44 (01): : 332 - 348

← 1 2 3 4 5 →

A Numerical Iterative Scheme for Solving Nonlinear Boundary Value Problems of Fractional Order 0 &lt; α &lt; 1

A Numerical Iterative Scheme for Solving Nonlinear Boundary Value Problems of Fractional Order 0 < α < 1