Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations
► Nonexistence of periodic solutions to fractional differential equations is firstly shown. ► Existence and uniqueness of S(Sv)-asymptotically T-periodic solutions to fractional differential equations are presented. ► More interesting results are extended to a subset of a Fréchet space. Using the fi...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2013-02, Vol.18 (2), p.246-256 |
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| container_title | Communications in nonlinear science & numerical simulation |
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| creator | Wang, JinRong Fec˘kan, Michal Zhou, Yong |
| description | ► Nonexistence of periodic solutions to fractional differential equations is firstly shown. ► Existence and uniqueness of S(Sv)-asymptotically T-periodic solutions to fractional differential equations are presented. ► More interesting results are extended to a subset of a Fréchet space.
Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results. |
| doi_str_mv | 10.1016/j.cnsns.2012.07.004 |
| format | Article |
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Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2012.07.004</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Asymptotic properties ; Asymptotically periodic solution ; Cauchy problem ; Computer simulation ; Differential equations ; Existence ; Fractional differential equations ; Laplace transforms ; Mathematical models ; Periodic functions ; Uniqueness</subject><ispartof>Communications in nonlinear science & numerical simulation, 2013-02, Vol.18 (2), p.246-256</ispartof><rights>2012 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-e0561f3c3c18081072ca394f6718ca9e092506c44ee1e924bdbadbe91aeb78d53</citedby><cites>FETCH-LOGICAL-c336t-e0561f3c3c18081072ca394f6718ca9e092506c44ee1e924bdbadbe91aeb78d53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cnsns.2012.07.004$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Wang, JinRong</creatorcontrib><creatorcontrib>Fec˘kan, Michal</creatorcontrib><creatorcontrib>Zhou, Yong</creatorcontrib><title>Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations</title><title>Communications in nonlinear science & numerical simulation</title><description>► Nonexistence of periodic solutions to fractional differential equations is firstly shown. ► Existence and uniqueness of S(Sv)-asymptotically T-periodic solutions to fractional differential equations are presented. ► More interesting results are extended to a subset of a Fréchet space.
Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results.</description><subject>Asymptotic properties</subject><subject>Asymptotically periodic solution</subject><subject>Cauchy problem</subject><subject>Computer simulation</subject><subject>Differential equations</subject><subject>Existence</subject><subject>Fractional differential equations</subject><subject>Laplace transforms</subject><subject>Mathematical models</subject><subject>Periodic functions</subject><subject>Uniqueness</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEuXjF7BkZEk4x06cDAyo4kuqYIHZcpyz5Cq1W9tB9N-TtIyI6e6Vnvekewi5oVBQoPXdutAuuliUQMsCRAHAT8iCNqLJRSn46bQDiLwSwM_JRYxrmFptxRfEvXmH3zYmdBozb7ItBut7q7PohzFZ72KmXJ-puN9sk09Wq2HY_0UZHzITlJ6TGrLeGoMBXbJTwN2oDtQVOTNqiHj9Oy_J59Pjx_IlX70_vy4fVrlmrE45QlVTwzTTtIGGgii1Yi03taCNVi1CW1ZQa84RKbYl7_pO9R22VGEnmr5il-T2eHcb_G7EmOTGRo3DoBz6MUpKWV1VtIVyQtkR1cHHGNDIbbAbFfaSgpztyrU82JWzXQlCTnan1v2xhdMXXxaDjNrODnsbUCfZe_tv_wcJzYfp</recordid><startdate>201302</startdate><enddate>201302</enddate><creator>Wang, JinRong</creator><creator>Fec˘kan, Michal</creator><creator>Zhou, Yong</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201302</creationdate><title>Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations</title><author>Wang, JinRong ; Fec˘kan, Michal ; Zhou, Yong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-e0561f3c3c18081072ca394f6718ca9e092506c44ee1e924bdbadbe91aeb78d53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Asymptotic properties</topic><topic>Asymptotically periodic solution</topic><topic>Cauchy problem</topic><topic>Computer simulation</topic><topic>Differential equations</topic><topic>Existence</topic><topic>Fractional differential equations</topic><topic>Laplace transforms</topic><topic>Mathematical models</topic><topic>Periodic functions</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, JinRong</creatorcontrib><creatorcontrib>Fec˘kan, Michal</creatorcontrib><creatorcontrib>Zhou, Yong</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, JinRong</au><au>Fec˘kan, Michal</au><au>Zhou, Yong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2013-02</date><risdate>2013</risdate><volume>18</volume><issue>2</issue><spage>246</spage><epage>256</epage><pages>246-256</pages><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>► Nonexistence of periodic solutions to fractional differential equations is firstly shown. ► Existence and uniqueness of S(Sv)-asymptotically T-periodic solutions to fractional differential equations are presented. ► More interesting results are extended to a subset of a Fréchet space.
Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2012.07.004</doi><tpages>11</tpages></addata></record> |
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| subjects | Asymptotic properties Asymptotically periodic solution Cauchy problem Computer simulation Differential equations Existence Fractional differential equations Laplace transforms Mathematical models Periodic functions Uniqueness |
| title | Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations |
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