Some properties of fractional burgers equation
The fractional generalization of a one‐dimensional Burgers equationwith initial conditions ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particul...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2002-06-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9838 |
| _version_ | 1818765347377905664 |
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| author | P. Miškinis |
| author_facet | P. Miškinis |
| author_sort | P. Miškinis |
| collection | DOAJ |
| description | The fractional generalization of a one‐dimensional Burgers equationwith initial conditions ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed.
Kai kurios trupmeninės Biurgerso lygtie savybės
Santrauka
Pasiublytas trupmeninis vienmates Biurgerso lygties apibendrinimassu pradinemis salygomis ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), kur ɸ = ɸ(x,t) ∈ C2(Ω): δɸ/δt; aDx p yra Rymano bei Liuvilio trupmenine p eiles išvestine; Ω = (x,t) : x ∈ E 1, t > 0;: bei šios lygties atskiras analitinis sprendinys. Nagrinejamas impulso bei energijos tvermes desniu atitinkami apibendrinimai, saryšis su paprasta Biurgerso lygtimi ir trupmenines Hopfo bei Koulo transformacijos savybes.
First Published Online: 14 Oct 2010 |
| first_indexed | 2024-12-18T08:16:39Z |
| format | Article |
| id | doaj.art-a844539c4b3b41f2ab4ab6c1ce16c47a |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-18T08:16:39Z |
| publishDate | 2002-06-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-a844539c4b3b41f2ab4ab6c1ce16c47a2022-12-21T21:14:48ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102002-06-017110.3846/13926292.2002.9637187Some properties of fractional burgers equationP. Miškinis0Department of Physics, Faculty of Fundamental Sciences , Vilnius Gediminas Technical University , Sauletekio Ave 11, Vilnius, LT‐2040, LithuaniaThe fractional generalization of a one‐dimensional Burgers equationwith initial conditions ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed. Kai kurios trupmeninės Biurgerso lygtie savybės Santrauka Pasiublytas trupmeninis vienmates Biurgerso lygties apibendrinimassu pradinemis salygomis ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), kur ɸ = ɸ(x,t) ∈ C2(Ω): δɸ/δt; aDx p yra Rymano bei Liuvilio trupmenine p eiles išvestine; Ω = (x,t) : x ∈ E 1, t > 0;: bei šios lygties atskiras analitinis sprendinys. Nagrinejamas impulso bei energijos tvermes desniu atitinkami apibendrinimai, saryšis su paprasta Biurgerso lygtimi ir trupmenines Hopfo bei Koulo transformacijos savybes. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/9838- |
| spellingShingle | P. Miškinis Some properties of fractional burgers equation Mathematical Modelling and Analysis - |
| title | Some properties of fractional burgers equation |
| title_full | Some properties of fractional burgers equation |
| title_fullStr | Some properties of fractional burgers equation |
| title_full_unstemmed | Some properties of fractional burgers equation |
| title_short | Some properties of fractional burgers equation |
| title_sort | some properties of fractional burgers equation |
| topic | - |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/9838 |
| work_keys_str_mv | AT pmiskinis somepropertiesoffractionalburgersequation |