Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative

Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative

In this paper, we deal with two fractional boundary value problems which have linear growth and quadratic growth about the fractional derivative in the nonlinearity term. By using variational methods coupled with the iterative methods, we obtain the existence results of solutions. To the best of the...

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Main Authors: Yaning Li, Quanguo Zhang, Baoyan Sun
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/7139795
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spelling doaj-43e000d673314d6da7a36c3e0b5b7c282020-11-25T03:50:10ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/71397957139795Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional DerivativeYaning Li0Quanguo Zhang1Baoyan Sun2College of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044, ChinaDepartment of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, ChinaSchool of Mathematics and Information Sciences, Yantai University, Yantai, Shandong 264005, ChinaIn this paper, we deal with two fractional boundary value problems which have linear growth and quadratic growth about the fractional derivative in the nonlinearity term. By using variational methods coupled with the iterative methods, we obtain the existence results of solutions. To the best of the authors’ knowledge, there are no results on the solutions to the fractional boundary problem which have quadratic growth about the fractional derivative in the nonlinearity term.http://dx.doi.org/10.1155/2020/7139795
collection DOAJ
language English
format Article
sources DOAJ
author Yaning Li
Quanguo Zhang
Baoyan Sun
spellingShingle Yaning Li
Quanguo Zhang
Baoyan Sun
Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative
Journal of Function Spaces
author_facet Yaning Li
Quanguo Zhang
Baoyan Sun
author_sort Yaning Li
title Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative
title_short Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative
title_full Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative
title_fullStr Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative
title_full_unstemmed Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative
title_sort existence of solutions for fractional boundary value problems with a quadratic growth of fractional derivative
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description In this paper, we deal with two fractional boundary value problems which have linear growth and quadratic growth about the fractional derivative in the nonlinearity term. By using variational methods coupled with the iterative methods, we obtain the existence results of solutions. To the best of the authors’ knowledge, there are no results on the solutions to the fractional boundary problem which have quadratic growth about the fractional derivative in the nonlinearity term.
url http://dx.doi.org/10.1155/2020/7139795
work_keys_str_mv AT yaningli existenceofsolutionsforfractionalboundaryvalueproblemswithaquadraticgrowthoffractionalderivative
AT quanguozhang existenceofsolutionsforfractionalboundaryvalueproblemswithaquadraticgrowthoffractionalderivative
AT baoyansun existenceofsolutionsforfractionalboundaryvalueproblemswithaquadraticgrowthoffractionalderivative
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