Monotone iterative method for two-point fractional boundary value problems

Monotone iterative method for two-point fractional boundary value problems

Abstract In this work, we deal with two-point Riemann–Liouville fractional boundary value problems. Firstly, we establish a new comparison principle. Then, we show the existence of extremal solutions for the two-point Riemann–Liouville fractional boundary value problems, using the method of upper an...

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Main Authors: Bo Tang, Jing Zhao, Zhenhai Liu
Format: Article
Language:English
Published: SpringerOpen 2018-05-01
Series:Advances in Difference Equations
Subjects:
Riemann–Liouville derivative
Boundary value problem
Upper and lower solutions
Maximal and minimal solutions
Online Access:http://link.springer.com/article/10.1186/s13662-018-1632-9
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spelling doaj-bb47c4e7ea224313a1967c9f621f325e2020-11-25T00:37:36ZengSpringerOpenAdvances in Difference Equations1687-18472018-05-01201811910.1186/s13662-018-1632-9Monotone iterative method for two-point fractional boundary value problemsBo Tang0Jing Zhao1Zhenhai Liu2Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for NationalitiesCollege of Sciences, Qinzhou UniversityGuangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for NationalitiesAbstract In this work, we deal with two-point Riemann–Liouville fractional boundary value problems. Firstly, we establish a new comparison principle. Then, we show the existence of extremal solutions for the two-point Riemann–Liouville fractional boundary value problems, using the method of upper and lower solutions. The performance of the approach is tested through a numerical example.http://link.springer.com/article/10.1186/s13662-018-1632-9Riemann–Liouville derivativeBoundary value problemUpper and lower solutionsMaximal and minimal solutions
collection DOAJ
language English
format Article
sources DOAJ
author Bo Tang
Jing Zhao
Zhenhai Liu
spellingShingle Bo Tang
Jing Zhao
Zhenhai Liu
Monotone iterative method for two-point fractional boundary value problems
Advances in Difference Equations
Riemann–Liouville derivative
Boundary value problem
Upper and lower solutions
Maximal and minimal solutions
author_facet Bo Tang
Jing Zhao
Zhenhai Liu
author_sort Bo Tang
title Monotone iterative method for two-point fractional boundary value problems
title_short Monotone iterative method for two-point fractional boundary value problems
title_full Monotone iterative method for two-point fractional boundary value problems
title_fullStr Monotone iterative method for two-point fractional boundary value problems
title_full_unstemmed Monotone iterative method for two-point fractional boundary value problems
title_sort monotone iterative method for two-point fractional boundary value problems
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2018-05-01
description Abstract In this work, we deal with two-point Riemann–Liouville fractional boundary value problems. Firstly, we establish a new comparison principle. Then, we show the existence of extremal solutions for the two-point Riemann–Liouville fractional boundary value problems, using the method of upper and lower solutions. The performance of the approach is tested through a numerical example.
topic Riemann–Liouville derivative
Boundary value problem
Upper and lower solutions
Maximal and minimal solutions
url http://link.springer.com/article/10.1186/s13662-018-1632-9
work_keys_str_mv AT botang monotoneiterativemethodfortwopointfractionalboundaryvalueproblems
AT jingzhao monotoneiterativemethodfortwopointfractionalboundaryvalueproblems
AT zhenhailiu monotoneiterativemethodfortwopointfractionalboundaryvalueproblems
_version_ 1725300523503976448

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