Quasilinearization method via lower and upper solutions for riemann-liouville fractional differential equations

Zachary Denton; P. W. Ng; A. S. Vatsala

Quasilinearization method via lower and upper solutions for riemann-liouville fractional differential equations

Zachary Denton
, P. W. Ng
, A. S. Vatsala

Mathematics and Statistics

University of Louisiana Lafayette

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, o < q < 1, are recalled and modified where necessary. Generalized quasilinearization method is developed for nonlinear fractional differential equations of order q, using upper and lower solutions. Quadratic convergence to the unique solution is proved via weighted sequences. © 2011 InforMath Publishing Group.

Original language	English
Pages (from-to)	239-251
Number of pages	13
Journal	Nonlinear Dynamics and Systems Theory
Volume	11
Issue number	3
State	Published - Oct 11 2011

Keywords

Fractional differential equations
Lower and upper solutions
Quasilinearization method

Cite this

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title = "Quasilinearization method via lower and upper solutions for riemann-liouville fractional differential equations",

abstract = "Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, o < q < 1, are recalled and modified where necessary. Generalized quasilinearization method is developed for nonlinear fractional differential equations of order q, using upper and lower solutions. Quadratic convergence to the unique solution is proved via weighted sequences. {\textcopyright} 2011 InforMath Publishing Group.",

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AU - Denton, Zachary

AU - Ng, P. W.

AU - Vatsala, A. S.

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Y1 - 2011/10/11

N2 - Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, o < q < 1, are recalled and modified where necessary. Generalized quasilinearization method is developed for nonlinear fractional differential equations of order q, using upper and lower solutions. Quadratic convergence to the unique solution is proved via weighted sequences. © 2011 InforMath Publishing Group.

AB - Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, o < q < 1, are recalled and modified where necessary. Generalized quasilinearization method is developed for nonlinear fractional differential equations of order q, using upper and lower solutions. Quadratic convergence to the unique solution is proved via weighted sequences. © 2011 InforMath Publishing Group.

KW - Fractional differential equations

KW - Lower and upper solutions

KW - Quasilinearization method

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JF - Nonlinear Dynamics and Systems Theory

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ER -

Quasilinearization method via lower and upper solutions for riemann-liouville fractional differential equations

Abstract

Keywords

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