Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space
In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1545043 |
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| author | Kangqun Zhang |
| author_facet | Kangqun Zhang |
| author_sort | Kangqun Zhang |
| collection | DOAJ |
| description | In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time. |
| format | Article |
| id | doaj-art-f7d6aaada46e49ba983b1bd3f1824129 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f7d6aaada46e49ba983b1bd3f18241292025-02-03T01:05:24ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/15450431545043Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev SpaceKangqun Zhang0Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, ChinaIn this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time.http://dx.doi.org/10.1155/2020/1545043 |
| spellingShingle | Kangqun Zhang Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space Advances in Mathematical Physics |
| title | Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space |
| title_full | Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space |
| title_fullStr | Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space |
| title_full_unstemmed | Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space |
| title_short | Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space |
| title_sort | existence of solution of space time fractional diffusion wave equation in weighted sobolev space |
| url | http://dx.doi.org/10.1155/2020/1545043 |
| work_keys_str_mv | AT kangqunzhang existenceofsolutionofspacetimefractionaldiffusionwaveequationinweightedsobolevspace |