Fractional evolution equation with Cauchy data in Lp spaces
In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in L 2 and H s . However, there have not been any papers dealing with...
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| Veröffentlicht in: | Boundary value problems 2022-12, Vol.2022 (1), p.100 |
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| creator | Phuong, Nguyen Duc Baleanu, Dumitru Agarwal, Ravi P. Long, Le Dinh |
| description | In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in
L
2
and
H
s
. However, there have not been any papers dealing with this problem with observed data in
L
p
with
p
≠
2
. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in
L
p
. To our knowledge,
L
p
evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem. |
| doi_str_mv | 10.1186/s13661-022-01683-1 |
| format | Article |
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L
2
and
H
s
. However, there have not been any papers dealing with this problem with observed data in
L
p
with
p
≠
2
. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in
L
p
. To our knowledge,
L
p
evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.</description><identifier>ISSN: 1687-2762</identifier><identifier>EISSN: 1687-2770</identifier><identifier>DOI: 10.1186/s13661-022-01683-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Approximations and Expansions ; Boundary value problems ; Cauchy problems ; Difference and Functional Equations ; Evolution ; Exact solutions ; Inverse problems ; Mathematical analysis ; Mathematicians ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations ; Smoothness</subject><ispartof>Boundary value problems, 2022-12, Vol.2022 (1), p.100</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p157t-47e361444041a1f13e1d7e244256088c9778ef32526c02c47d39ffcbd29e628b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1186/s13661-022-01683-1$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1186/s13661-022-01683-1$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,860,27901,27902,41096,41464,42165,42533,51294,51551</link.rule.ids></links><search><creatorcontrib>Phuong, Nguyen Duc</creatorcontrib><creatorcontrib>Baleanu, Dumitru</creatorcontrib><creatorcontrib>Agarwal, Ravi P.</creatorcontrib><creatorcontrib>Long, Le Dinh</creatorcontrib><title>Fractional evolution equation with Cauchy data in Lp spaces</title><title>Boundary value problems</title><addtitle>Bound Value Probl</addtitle><description>In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in
L
2
and
H
s
. However, there have not been any papers dealing with this problem with observed data in
L
p
with
p
≠
2
. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in
L
p
. To our knowledge,
L
p
evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.</description><subject>Analysis</subject><subject>Approximations and Expansions</subject><subject>Boundary value problems</subject><subject>Cauchy problems</subject><subject>Difference and Functional Equations</subject><subject>Evolution</subject><subject>Exact solutions</subject><subject>Inverse problems</subject><subject>Mathematical analysis</subject><subject>Mathematicians</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Smoothness</subject><issn>1687-2762</issn><issn>1687-2770</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNpFkMFLwzAUh4MoOKf_gKeA52jeS5qkeJLiVCjsMs8hS1PXUdquaRX_e7tV9PS-w8ePx0fILfB7AKMeIgilgHFExkEZweCMLCbQDLXm53-s8JJcxbjnXKRC4oI8rnrnh6ptXE3DZ1uPR6bhMLoTfFXDjmZu9LtvWrjB0aqheUdj53yI1-SidHUMN793Sd5Xz5vsleXrl7fsKWcdJHpgUgehQErJJTgoQQQodEApMVHcGJ9qbUIpMEHlOXqpC5GWpd8WmAaFZiuW5G7e7fr2MIY42H079tPH0aJOJE7j3EyWmK3Y9VXzEfp_C7g9VrJzJTtVsqdKFsQPirxYsQ</recordid><startdate>20221214</startdate><enddate>20221214</enddate><creator>Phuong, Nguyen Duc</creator><creator>Baleanu, Dumitru</creator><creator>Agarwal, Ravi P.</creator><creator>Long, Le Dinh</creator><general>Springer International Publishing</general><general>Hindawi Limited</general><scope>C6C</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20221214</creationdate><title>Fractional evolution equation with Cauchy data in Lp spaces</title><author>Phuong, Nguyen Duc ; Baleanu, Dumitru ; Agarwal, Ravi P. ; Long, Le Dinh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-47e361444041a1f13e1d7e244256088c9778ef32526c02c47d39ffcbd29e628b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Analysis</topic><topic>Approximations and Expansions</topic><topic>Boundary value problems</topic><topic>Cauchy problems</topic><topic>Difference and Functional Equations</topic><topic>Evolution</topic><topic>Exact solutions</topic><topic>Inverse problems</topic><topic>Mathematical analysis</topic><topic>Mathematicians</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Smoothness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Phuong, Nguyen Duc</creatorcontrib><creatorcontrib>Baleanu, Dumitru</creatorcontrib><creatorcontrib>Agarwal, Ravi P.</creatorcontrib><creatorcontrib>Long, Le Dinh</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Boundary value problems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Phuong, Nguyen Duc</au><au>Baleanu, Dumitru</au><au>Agarwal, Ravi P.</au><au>Long, Le Dinh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractional evolution equation with Cauchy data in Lp spaces</atitle><jtitle>Boundary value problems</jtitle><stitle>Bound Value Probl</stitle><date>2022-12-14</date><risdate>2022</risdate><volume>2022</volume><issue>1</issue><spage>100</spage><pages>100-</pages><issn>1687-2762</issn><eissn>1687-2770</eissn><abstract>In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in
L
2
and
H
s
. However, there have not been any papers dealing with this problem with observed data in
L
p
with
p
≠
2
. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in
L
p
. To our knowledge,
L
p
evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13661-022-01683-1</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Analysis Approximations and Expansions Boundary value problems Cauchy problems Difference and Functional Equations Evolution Exact solutions Inverse problems Mathematical analysis Mathematicians Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Smoothness |
| title | Fractional evolution equation with Cauchy data in Lp spaces |
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