Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition
In this article, by using topological degree theory couple with the method of lower and upper solutions, we study the existence of at least three solutions to Riemann-Stieltjes integral initial value problem of the type Dαx(t)=f(t,x), t∈[0,1], x(0)=∫01x(t)dA(t), where Dαx(t) is the standard conform...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/8402347 |
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| author | Shuman Meng Yujun Cui |
| author_facet | Shuman Meng Yujun Cui |
| author_sort | Shuman Meng |
| collection | DOAJ |
| description | In this article, by using topological degree theory couple with the method of lower and upper solutions, we study the existence of at least three solutions to Riemann-Stieltjes integral initial value problem of the type Dαx(t)=f(t,x), t∈[0,1], x(0)=∫01x(t)dA(t), where Dαx(t) is the standard conformable fractional derivative of order α, 0<α≤1, and f∈C([0,1]×R,R). Simultaneously, the fixed point theorem for set-valued increasing operator is applied when considering the given problem. |
| format | Article |
| id | doaj-art-37461ea58f2949cda1e2b257d35eaedb |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-37461ea58f2949cda1e2b257d35eaedb2025-02-03T07:25:01ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/84023478402347Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary ConditionShuman Meng0Yujun Cui1Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266590, ChinaState Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this article, by using topological degree theory couple with the method of lower and upper solutions, we study the existence of at least three solutions to Riemann-Stieltjes integral initial value problem of the type Dαx(t)=f(t,x), t∈[0,1], x(0)=∫01x(t)dA(t), where Dαx(t) is the standard conformable fractional derivative of order α, 0<α≤1, and f∈C([0,1]×R,R). Simultaneously, the fixed point theorem for set-valued increasing operator is applied when considering the given problem.http://dx.doi.org/10.1155/2019/8402347 |
| spellingShingle | Shuman Meng Yujun Cui Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition Complexity |
| title | Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition |
| title_full | Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition |
| title_fullStr | Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition |
| title_full_unstemmed | Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition |
| title_short | Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition |
| title_sort | multiplicity results to a conformable fractional differential equations involving integral boundary condition |
| url | http://dx.doi.org/10.1155/2019/8402347 |
| work_keys_str_mv | AT shumanmeng multiplicityresultstoaconformablefractionaldifferentialequationsinvolvingintegralboundarycondition AT yujuncui multiplicityresultstoaconformablefractionaldifferentialequationsinvolvingintegralboundarycondition |