Fractional telegraph equation under moving time-harmonic impact
•The time-fractional telegraph equation with moving time-harmonic source is considered on a real line.•Two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives...
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| Veröffentlicht in: | International journal of heat and mass transfer 2022-01, Vol.182, p.121958, Article 121958 |
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| container_title | International journal of heat and mass transfer |
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| creator | Povstenko, Yuriy Ostoja-Starzewski, Martin |
| description | •The time-fractional telegraph equation with moving time-harmonic source is considered on a real line.•Two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives are investigated.•The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation.•For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term.•The derived solutions can be successfully used when the source term can be expanded into a Fourier series.
The time-fractional telegraph equation with moving time-harmonic source is considered on a real line. We investigate two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives. In both cases the order of fractional derivative 1 |
| doi_str_mv | 10.1016/j.ijheatmasstransfer.2021.121958 |
| format | Article |
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The time-fractional telegraph equation with moving time-harmonic source is considered on a real line. We investigate two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives. In both cases the order of fractional derivative 1<α<2. For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term. The considered problem is solved using the integral transforms technique. The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation. Numerical results are illustrated graphically for different values of nondimensional parameters.</description><identifier>ISSN: 0017-9310</identifier><identifier>EISSN: 1879-2189</identifier><identifier>DOI: 10.1016/j.ijheatmasstransfer.2021.121958</identifier><identifier>PMID: 36777796</identifier><language>eng</language><publisher>England: Elsevier Ltd</publisher><subject>Caputo derivative ; Doppler effect ; Fourier transform ; Fractional calculus ; Integral transforms ; Laplace transform ; Telegraph equation ; Time-harmonic impact ; Wave fronts</subject><ispartof>International journal of heat and mass transfer, 2022-01, Vol.182, p.121958, Article 121958</ispartof><rights>2021 Elsevier Ltd</rights><rights>Copyright Elsevier BV Jan 2022</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c484t-12455d6ef704a53fb0d0dc01933a5e59a315646f6b7304fa38a46303cc13d27b3</citedby><cites>FETCH-LOGICAL-c484t-12455d6ef704a53fb0d0dc01933a5e59a315646f6b7304fa38a46303cc13d27b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0017931021010632$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/36777796$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Povstenko, Yuriy</creatorcontrib><creatorcontrib>Ostoja-Starzewski, Martin</creatorcontrib><title>Fractional telegraph equation under moving time-harmonic impact</title><title>International journal of heat and mass transfer</title><addtitle>Int J Heat Mass Transf</addtitle><description>•The time-fractional telegraph equation with moving time-harmonic source is considered on a real line.•Two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives are investigated.•The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation.•For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term.•The derived solutions can be successfully used when the source term can be expanded into a Fourier series.
The time-fractional telegraph equation with moving time-harmonic source is considered on a real line. We investigate two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives. In both cases the order of fractional derivative 1<α<2. For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term. The considered problem is solved using the integral transforms technique. The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation. Numerical results are illustrated graphically for different values of nondimensional parameters.</description><subject>Caputo derivative</subject><subject>Doppler effect</subject><subject>Fourier transform</subject><subject>Fractional calculus</subject><subject>Integral transforms</subject><subject>Laplace transform</subject><subject>Telegraph equation</subject><subject>Time-harmonic impact</subject><subject>Wave fronts</subject><issn>0017-9310</issn><issn>1879-2189</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNqNkD1PwzAQhi0EoqXwF1Akli4Jdhw78QSoonyoEgvMluNcWkf5aO2kEv8eRy0MsODlZOu593wPQnOCI4IJv60iU21A9Y1yrreqdSXYKMYxiUhMBMtO0JRkqQhjkolTNMWYpKGgBE_QhXPVeMUJP0cTylN_BJ-iu6VVujddq-qghxrWVm03AewGNT4GQ1uADZpub9p10JsGwo2yTdcaHZhm6zsv0VmpagdXxzpDH8vH98VzuHp7elk8rEKdZEkfkjhhrOBQ-g8oRsscF7jQmAhKFQMmFCWMJ7zkeUpxUiqaqYRTTLUmtIjTnM7Q_JC7td1uANfLxjgNda1a6AYn4zRlgiWYUY_e_EKrbrB-QU9xwmOKBcOeuj9Q2nbOWSjl1ppG2U9JsBxly0r-lS1H2fIg20dcHwcNeQPFT8C3XQ-8HgDwZvbGtzttoNVQGAu6l0Vn_j_tC5ram6g</recordid><startdate>202201</startdate><enddate>202201</enddate><creator>Povstenko, Yuriy</creator><creator>Ostoja-Starzewski, Martin</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope><scope>7X8</scope></search><sort><creationdate>202201</creationdate><title>Fractional telegraph equation under moving time-harmonic impact</title><author>Povstenko, Yuriy ; Ostoja-Starzewski, Martin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c484t-12455d6ef704a53fb0d0dc01933a5e59a315646f6b7304fa38a46303cc13d27b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Caputo derivative</topic><topic>Doppler effect</topic><topic>Fourier transform</topic><topic>Fractional calculus</topic><topic>Integral transforms</topic><topic>Laplace transform</topic><topic>Telegraph equation</topic><topic>Time-harmonic impact</topic><topic>Wave fronts</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Povstenko, Yuriy</creatorcontrib><creatorcontrib>Ostoja-Starzewski, Martin</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>International journal of heat and mass transfer</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Povstenko, Yuriy</au><au>Ostoja-Starzewski, Martin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractional telegraph equation under moving time-harmonic impact</atitle><jtitle>International journal of heat and mass transfer</jtitle><addtitle>Int J Heat Mass Transf</addtitle><date>2022-01</date><risdate>2022</risdate><volume>182</volume><spage>121958</spage><pages>121958-</pages><artnum>121958</artnum><issn>0017-9310</issn><eissn>1879-2189</eissn><abstract>•The time-fractional telegraph equation with moving time-harmonic source is considered on a real line.•Two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives are investigated.•The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation.•For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term.•The derived solutions can be successfully used when the source term can be expanded into a Fourier series.
The time-fractional telegraph equation with moving time-harmonic source is considered on a real line. We investigate two characteristic versions of this equation: the “wave-type” with the second and Caputo fractional time-derivatives as well as the “heat-type” with the first and Caputo fractional time-derivatives. In both cases the order of fractional derivative 1<α<2. For the time-fractional telegraph equation it is impossible to consider the quasi-steady-state corresponding to the solution being a product of a function of the spatial coordinate and the time-harmonic term. The considered problem is solved using the integral transforms technique. The solution to the “wave-type” equation contains wave fronts and describes the Doppler effect contrary to the solution for the “heat-type” equation. Numerical results are illustrated graphically for different values of nondimensional parameters.</abstract><cop>England</cop><pub>Elsevier Ltd</pub><pmid>36777796</pmid><doi>10.1016/j.ijheatmasstransfer.2021.121958</doi><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals |
| subjects | Caputo derivative Doppler effect Fourier transform Fractional calculus Integral transforms Laplace transform Telegraph equation Time-harmonic impact Wave fronts |
| title | Fractional telegraph equation under moving time-harmonic impact |
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