An inverse source problem for a two-parameter anomalous diffusion with local time datum
We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a series representation of the solution and the source term. Th...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2017-03, Vol.73 (6), p.1008-1015 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Furati, Khaled M. Iyiola, Olaniyi S. Mustapha, Kassem |
| description | We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a series representation of the solution and the source term. The two local time conditions spare us from measuring the fractional integral initial conditions commonly associated with fractional derivatives. On the other hand, they lead to delicate 2×2 linear systems for the Fourier coefficients of the source term and of the fractional integral of the solution at t=0. The asymptotic behavior and estimates of the generalized Mittag-Leffler function are used to establish the solvability of these linear systems, and to obtain sufficient conditions for the existence of our construction. Analytical and numerical examples are provided. |
| doi_str_mv | 10.1016/j.camwa.2016.06.036 |
| format | Article |
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Analytical and numerical examples are provided.</description><subject>Asymptotic methods</subject><subject>Boundary conditions</subject><subject>Differential equations</subject><subject>Fourier analysis</subject><subject>Fractional diffusion</subject><subject>Hilfer derivative</subject><subject>Initial conditions</subject><subject>Integrals</subject><subject>Inverse source problem</subject><subject>Linear systems</subject><subject>Mittag-Leffler function</subject><subject>Studies</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LxDAUDKLguvoLvAQ8tyZNNm0OHpbFL1jwongMafKKKW2zJuku_nuj61l48BiYmfdmELqmpKSEitu-NHo86LLKoCR5mDhBC9rUrKiFaE7RgjSyKWhV0XN0EWNPCOGsIgv0vp6wm_YQIuDo52AA74JvBxhx5wPWOB18sdNBj5Ag48mPevBzxNZ13Rydn_DBpQ88eKMHnNwI2Oo0j5forNNDhKu_vURvD_evm6di-_L4vFlvC8NqkYrOct62lDG5As64blqpBWNQd0ChFVoK2poVZy0Fw8FKWVmtmSHNqra24pwt0c3RN3_9OUNMqs8ppnxSUVnV2ZlLllnsyDLBxxigU7vgRh2-FCXqp0HVq98G1U-DiuRhIqvujirIAfYOgorGwWTAugAmKevdv_pv6xF7sA</recordid><startdate>20170315</startdate><enddate>20170315</enddate><creator>Furati, Khaled M.</creator><creator>Iyiola, Olaniyi S.</creator><creator>Mustapha, Kassem</creator><general>Elsevier Ltd</general><general>Elsevier BV</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>20170315</creationdate><title>An inverse source problem for a two-parameter anomalous diffusion with local time datum</title><author>Furati, Khaled M. ; Iyiola, Olaniyi S. ; Mustapha, Kassem</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c376t-fd44bb13395e434a8b9a633e7fe1eb6a961bc543b1ec4ed992daa3c0857dd2443</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Asymptotic methods</topic><topic>Boundary conditions</topic><topic>Differential equations</topic><topic>Fourier analysis</topic><topic>Fractional diffusion</topic><topic>Hilfer derivative</topic><topic>Initial conditions</topic><topic>Integrals</topic><topic>Inverse source problem</topic><topic>Linear systems</topic><topic>Mittag-Leffler function</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Furati, Khaled M.</creatorcontrib><creatorcontrib>Iyiola, Olaniyi S.</creatorcontrib><creatorcontrib>Mustapha, Kassem</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>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Furati, Khaled M.</au><au>Iyiola, Olaniyi S.</au><au>Mustapha, Kassem</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An inverse source problem for a two-parameter anomalous diffusion with local time datum</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2017-03-15</date><risdate>2017</risdate><volume>73</volume><issue>6</issue><spage>1008</spage><epage>1015</epage><pages>1008-1015</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. 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| ispartof | Computers & mathematics with applications (1987), 2017-03, Vol.73 (6), p.1008-1015 |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Asymptotic methods Boundary conditions Differential equations Fourier analysis Fractional diffusion Hilfer derivative Initial conditions Integrals Inverse source problem Linear systems Mittag-Leffler function Studies |
| title | An inverse source problem for a two-parameter anomalous diffusion with local time datum |
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