Nonlocal q-fractional boundary value problem with Stieltjes integral conditions
In this paper, we are dedicated to investigating a new class of one-dimensional lower-order fractional q-differential equations involving integral boundary conditions supplemented with Stieltjes integral. This condition is more general as it contains an arbitrary order derivative. It should be point...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2019-06-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.journals.vu.lt/nonlinear-analysis/article/view/12963 |
| _version_ | 1811331258254360576 |
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| author | Jing Ren Chengbo Zhai |
| author_facet | Jing Ren Chengbo Zhai |
| author_sort | Jing Ren |
| collection | DOAJ |
| description | In this paper, we are dedicated to investigating a new class of one-dimensional lower-order fractional q-differential equations involving integral boundary conditions supplemented with Stieltjes integral. This condition is more general as it contains an arbitrary order derivative. It should be pointed out that the problem discussed in the current setting provides further insight into the research on nonlocal and integral boundary value problems. We first give the Green's functions of the boundary value problem and then develop some properties of the Green's functions that are conductive to our main results. Our main aim is to present two results: one considering the uniqueness of nontrivial solutions is given by virtue of contraction mapping principle associated with properties of u0-positive linear operator in which Lipschitz constant is associated with the first eigenvalue corresponding to related linear operator, while the other one aims to obtain the existence of multiple positive solutions under some appropriate conditions via standard fixed point theorems due to Krasnoselskii and Leggett–Williams. Finally, we give an example to illustrate the main results. |
| first_indexed | 2024-04-13T16:17:57Z |
| format | Article |
| id | doaj.art-343b8c53b2684da8a513511fe3012391 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-13T16:17:57Z |
| publishDate | 2019-06-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-343b8c53b2684da8a513511fe30123912022-12-22T02:40:01ZengVilnius University PressNonlinear Analysis1392-51132335-89632019-06-0124410.15388/NA.2019.4.6Nonlocal q-fractional boundary value problem with Stieltjes integral conditionsJing Ren0Chengbo Zhai1Shanxi UniversityShanxi UniversityIn this paper, we are dedicated to investigating a new class of one-dimensional lower-order fractional q-differential equations involving integral boundary conditions supplemented with Stieltjes integral. This condition is more general as it contains an arbitrary order derivative. It should be pointed out that the problem discussed in the current setting provides further insight into the research on nonlocal and integral boundary value problems. We first give the Green's functions of the boundary value problem and then develop some properties of the Green's functions that are conductive to our main results. Our main aim is to present two results: one considering the uniqueness of nontrivial solutions is given by virtue of contraction mapping principle associated with properties of u0-positive linear operator in which Lipschitz constant is associated with the first eigenvalue corresponding to related linear operator, while the other one aims to obtain the existence of multiple positive solutions under some appropriate conditions via standard fixed point theorems due to Krasnoselskii and Leggett–Williams. Finally, we give an example to illustrate the main results.http://www.journals.vu.lt/nonlinear-analysis/article/view/12963fractional q-difference equationsexistence and uniquenessintegral boundary conditions |
| spellingShingle | Jing Ren Chengbo Zhai Nonlocal q-fractional boundary value problem with Stieltjes integral conditions Nonlinear Analysis fractional q-difference equations existence and uniqueness integral boundary conditions |
| title | Nonlocal q-fractional boundary value problem with Stieltjes integral conditions |
| title_full | Nonlocal q-fractional boundary value problem with Stieltjes integral conditions |
| title_fullStr | Nonlocal q-fractional boundary value problem with Stieltjes integral conditions |
| title_full_unstemmed | Nonlocal q-fractional boundary value problem with Stieltjes integral conditions |
| title_short | Nonlocal q-fractional boundary value problem with Stieltjes integral conditions |
| title_sort | nonlocal q fractional boundary value problem with stieltjes integral conditions |
| topic | fractional q-difference equations existence and uniqueness integral boundary conditions |
| url | http://www.journals.vu.lt/nonlinear-analysis/article/view/12963 |
| work_keys_str_mv | AT jingren nonlocalqfractionalboundaryvalueproblemwithstieltjesintegralconditions AT chengbozhai nonlocalqfractionalboundaryvalueproblemwithstieltjesintegralconditions |