Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays
Abstract This paper is concerned with stochastic differential equations of fractional-order q ∈ ( m − 1 , m ) $q \in(m-1, m)$ (where m ∈ Z $m \in \mathbb{Z}$ and m ≥ 2 $m \geq 2$ ) with finite delay at a space B C ( [ − τ , 0 ] ; R d ) $BC ( [ - \tau, 0];R^{d} )$ . Some sufficient conditions are obt...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1169-3 |
| _version_ | 1819110239757139968 |
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| author | Xianmin Zhang Praveen Agarwal Zuohua Liu Hui Peng Fang You Yajun Zhu |
| author_facet | Xianmin Zhang Praveen Agarwal Zuohua Liu Hui Peng Fang You Yajun Zhu |
| author_sort | Xianmin Zhang |
| collection | DOAJ |
| description | Abstract This paper is concerned with stochastic differential equations of fractional-order q ∈ ( m − 1 , m ) $q \in(m-1, m)$ (where m ∈ Z $m \in \mathbb{Z}$ and m ≥ 2 $m \geq 2$ ) with finite delay at a space B C ( [ − τ , 0 ] ; R d ) $BC ( [ - \tau, 0];R^{d} )$ . Some sufficient conditions are obtained for the existence and uniqueness of solutions for these stochastic fractional differential systems by applying the Picard iterations method and the generalized Gronwall inequality. |
| first_indexed | 2024-12-22T03:38:34Z |
| format | Article |
| id | doaj.art-4debf7ad50fe4a3794ae54f5ece6404e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T03:38:34Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4debf7ad50fe4a3794ae54f5ece6404e2022-12-21T18:40:18ZengSpringerOpenAdvances in Difference Equations1687-18472017-04-012017111810.1186/s13662-017-1169-3Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delaysXianmin Zhang0Praveen Agarwal1Zuohua Liu2Hui Peng3Fang You4Yajun Zhu5School of Electronic Engineering, Jiujiang UniversityDepartment of Mathematics, Anand International College of EngineeringSchool of Chemistry and Chemical Engineering, Chongqing UniversitySchool of Electronic Engineering, Jiujiang UniversitySchool of Electronic Engineering, Jiujiang UniversitySchool of Electronic Engineering, Jiujiang UniversityAbstract This paper is concerned with stochastic differential equations of fractional-order q ∈ ( m − 1 , m ) $q \in(m-1, m)$ (where m ∈ Z $m \in \mathbb{Z}$ and m ≥ 2 $m \geq 2$ ) with finite delay at a space B C ( [ − τ , 0 ] ; R d ) $BC ( [ - \tau, 0];R^{d} )$ . Some sufficient conditions are obtained for the existence and uniqueness of solutions for these stochastic fractional differential systems by applying the Picard iterations method and the generalized Gronwall inequality.http://link.springer.com/article/10.1186/s13662-017-1169-3stochastic differential equationsstochastic fractional differential equationsexistence of solutionsfractional order |
| spellingShingle | Xianmin Zhang Praveen Agarwal Zuohua Liu Hui Peng Fang You Yajun Zhu Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays Advances in Difference Equations stochastic differential equations stochastic fractional differential equations existence of solutions fractional order |
| title | Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays |
| title_full | Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays |
| title_fullStr | Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays |
| title_full_unstemmed | Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays |
| title_short | Existence and uniqueness of solutions for stochastic differential equations of fractional-order q > 1 $q > 1$ with finite delays |
| title_sort | existence and uniqueness of solutions for stochastic differential equations of fractional order q 1 q 1 with finite delays |
| topic | stochastic differential equations stochastic fractional differential equations existence of solutions fractional order |
| url | http://link.springer.com/article/10.1186/s13662-017-1169-3 |
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