Strong solutions of a nonlinear degenerate fractional order evolution equation
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 61-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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Unique solvability conditions in the class of strong solutions are obtained for initial value problems to a degenerate evolution equation, not solvable with respect to the fractional derivative. General results are applied to research of an initial boundary value problem for the equations system describing the fractional model of viscoelastic Kelvin–Voigt fluid.
Keywords: degenerate evolution equation, fractional Caputo derivative, nonlinear equation, initial boundary value problem, fractional model of viscoelastic fluid.
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M. V. Plekhanova. Strong solutions of a nonlinear degenerate fractional order evolution equation. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 61-74. http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a5/

[1] Fedorov V. E., Gordievskikh D. M., “Resolving Operators of Degenerate Evolution Equations with Fractional Derivative with Respect to Time”, Russian Mathematics, 59:1 (2015), 60–70 | DOI

[2] D. M. Gordievskikh, V. E. Fedorov, “Solutions for initial boundary value problems for some degenerate equations systems of fractional order with respect to the time”, Izv. Irkut. Gos. Univ., 12 (2015), 12–22 (in Russian)

[3] Fedorov V. E., Gordievskikh D. M., Plekhanova M. V., “Equations in Banach Spaces with a Degenerate Operator under a Fractional Derivative”, Differ. Equ., 51:10 (2015), 1360–1368 | DOI

[4] G. V. Demidenko, G. V. Uspenskii, Equations and Systems That Are Not Solved for the Highest Derivative, Nauch. Kniga, Novosibirsk, 1998 (in Russian)

[5] Favini A., Yagi A., Degenerate Differential Equations in Banach Spaces, N.Y., 1999

[6] A. G. Sveshnikov, A. B. Al'shin, M. O. Korpusov, Yu. D. Pletner, Linear and Non-Linear Equations of Sobolev Type, M., 2007 (in Russian)

[7] Plekhanova M. V., “Quasilinear Equations that are not Solved for the Higher-Order Time Derivative”, Sib. Mat. J., 56:4 (2015), 725–735 | DOI

[8] Podlubny I., Fractional Differential Equations, San Diego–Boston, 1999

[9] Mainardi F., Spada G., “Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology”, The European Physical Journal, 193, Special Topics. Special issue: Perspectives on Fractional Dynamics and Control (2011), 133–160

[10] Uchaikin V. V., Fractional Derivatives for Phisicists and Engineers, Higher Education Press, Bejing, 2012

[11] Jaishankar A., McKinley G. H., “Power-Law Rheology in the Bulk and at the Interface: Quasi-Properties and Fractional Constitutive Equations”, Proc. R. Soc. A, 469 (2015), 20120284 | DOI

[12] Sviridyuk G. A., Fedorov V. E., Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003

[13] A. P. Oskolkov, “Initial-boundary value problems for equations of motion of Kelvin–Foygta and Oldroyd fluids”, Proc. Steklov Inst. Math., 179 (1989), 137–182

[14] O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, Science Publishers, New York–London–Paris, 1969