QUASILINEARIZATION APPLIED TO BOUNDARY VALUE PROBLEMS AT RESONANCE FOR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS

PAUL ELOE; JAGANMOHAN JONNALAGADDA

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QUASILINEARIZATION APPLIED TO BOUNDARY VALUE PROBLEMS AT RESONANCE FOR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS

机译：用于黎曼 - 荔道分数微分方程的共振时代的Quasilinearization应用于边值问题

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The quasilinearization method is applied to a boundary value problem at resonance for a Riemann-Liouville fractional differential equation. Under suitable hypotheses, the method of upper and lower solutions is employed to establish uniqueness of solutions. A shift method, coupled with the method of upper and lower solutions, is applied to establish existence of solutions. The quasilinearization algorithm is then applied to obtain sequences of lower and upper solutions that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance.

机译：Quasilinearization方法应用于Riemann-Liouville分数差分方程的共振下的边值问题。在合适的假设下，采用上下解决方案的方法来建立溶液的唯一性。耦合与上层和下解决方案的方法的换档方法应用于建立溶液的存在。然后应用Quasilinearization算法以获得较低和上溶液的序列，该序列可以单调地和二次地收敛到谐振时边值问题的独特解决方案。

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来源
《Discrete and continuous dynamical systems▼hSeries S》 |2020年第10期|2719-2734|共16页
作者
PAUL ELOE; JAGANMOHAN JONNALAGADDA;
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作者单位

Department of Mathematics University of Dayton Dayton OH 45469-2316 USA;

Department of Mathematics Birla Institute of Technology and Science Pilani Hyderabad-500078 Telangana India;

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原文格式 PDF
正文语种 eng
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关键词
Boundary value problem at resonance; Riemann-Liouville fractional differential equations; upper and lower solutions; quasilinearization;

机译：谐振边界值问题;riemann-liouville分数微分方程;上层和较低的解决方案;QuasilineArization.;

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1. Quasilinearization and Boundary Value Problems at Resonance for Caputo Fractional Differential Equations [J] . Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer Communications on applied nonlinear analysis . 2019,第3期

机译：Caputo分数阶微分方程共振的拟线性化和边值问题
2. Quasilinearization and Boundary Value Problems at Resonance for Caputo Fractional Differential Equations [J] . Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer Communications on applied nonlinear analysis . 2019,第3期

机译：Caputo分数微分方程共振的Quasilearization和边值问题
3. GENERALIZED EXTENSION OF THE QUASILINEARIZATION METHOD FOR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS [J] . ZACHARY DENTON Dynamic Systems and Applications . 2014,第2a3期

机译：RIEMANN-LIOUVILLE分数阶微分方程拟线性化方法的广义推广
4. The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives [C] . Arman Dabiri, Laya Karimi Annual American Control Conference . 2019

机译：Riemann-Liouville导数分数阶微分方程数值解的分数切比雪夫搭配方法
5. Qualitative Theory of Riemann-Liouville Fractional Differential Equations [D] . Denton, Zachary 2012

机译：黎曼-利维尔分数阶微分方程的定性理论
6. Existence and Uniqueness Theorems for Impulsive Fractional Differential Equations with the Two-Point and Integral Boundary Conditions [O] . M. J. Mardanov, N. I. Mahmudov, Y. A. Sharifov -1

机译：具有两点和积分边界条件的脉冲分数阶微分方程的存在性和唯一性定理
7. Quasilinearization for fractional differential equations of Riemann-Liouville type [O] . Zhenhai Liu, Rui Wang, Jing Zhao 2014

机译：黎曼 - 荔枝型型分数微分方程的QuasilineArization

QUASILINEARIZATION APPLIED TO BOUNDARY VALUE PROBLEMS AT RESONANCE FOR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS

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