Geodesic
Cauchy problem for high even order parabolic equation with time fractional derivative
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 696-706

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In the paper, we construct a fundamental solution for a higher order parabolic equation with time-fractional derivative and study its properties. We solve the Cauchy problem for the equation under study and prove a uniqueness theorem in the class of fast-growing functions.
Keywords: fundamental solution, Riemann–Liouville fractional derivative, Cauchy problem, high order equation. 
L. L. Karasheva. Cauchy problem for high even order parabolic equation with time fractional derivative. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 696-706. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a93/
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     title = {Cauchy problem for high even order parabolic equation with time fractional derivative},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a93/}
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[1] A. M. Nakhushev, Equations of mathematical biology, Vysshaya shkola, M., 1995 (Russian) | Zbl

[2] O. A. Ladyzhenskaya, “On the uniqueness of the solution of Cauchy's problem for a linear parabolic equation”, Mat. Sb., 27(69):2 (1950), 175–184 (Russian) | MR | Zbl

[3] L. Cattabriga, “Problemi al contorno per equazioni paraboliche di ordine 2n”, Rend. Semin. Mat. Univ. Padov, 28 (1958), 376–-401 | MR | Zbl

[4] A. N. Kochubei, “Fractional-order diffusion”, Differential Equations, 26:4 (1990), 485–-492 | MR | Zbl

[5] A. V. Pskhu, “The fundamental solution of a diffusion-wave equation of fractional order”, Izvestiya: Mathematics, 73:2 (2009), 351–392 | DOI | MR | Zbl

[6] O. P. Agrawal, “A general solution for a fourth-order fractional diffusion-wave equation defined in a bounded domain”, Computers and Structures, 79 (2001), 1497–1501 | DOI | MR

[7] A. A. Voroshilov, A. A. Kilbas, “The Cauchy problem for the diffusion-wave equation with the Caputo partial derivative”, Differential equations, 42:5 (2006), 638–-649 | DOI | MR | Zbl

[8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier, Amsterdam, 2006 | MR | Zbl

[9] A. V. Pskhu, Partial differential equations of fractional order, Nauka, M., 2005 (Russian) | MR | Zbl

[10] M. V. Plekhanova, “Start control problems for fractional order evolution equations”, Chelyab. Fiz.-Mat. Zh., 1:3 (2016), 15–-36 | MR

[11] E. A. Romanova, V. E. Fedorov, “Resolving operators of a linear degenerate evolution equation with Caputo derivative. The sectorial case”, Mathematical notes of NEFU, 23:4 (2016), 58–-72 | Zbl

[12] M. V. Plekhanova, “Solvability of control problems for degenerate evolution equations of fractional order”, Chelyab. Fiz.-Mat. Zh., 2:1 (2017), 53–-65 | MR

[13] E. M. Wright, “On the coefficients of power series having exponential singularities”, J. London Math. Soc., 8:1 (1933), 71–79 | DOI | MR | Zbl

[14] E. M. Wright, “The generalized Bessel function of order greater than one”, Quart. J. Math., Oxford Ser., 11 (1940), 36–48 | DOI | MR