Geodesic
Solutions for initial boundary value problems for some degenerate equations systems of fractional order with respect to the time
The Bulletin of Irkutsk State University. Series Mathematics, Tome 12 (2015), pp. 12-22

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Solvability theorem for the Cauchy problem to a degenerate linear evolution equation of fractional order in a Banach space is used for deriving of necessary and sufficient conditions of solvability for some arising in hydrodynamics equations systems of fractional order with respect to the time. Solutions forms for considered problems are obtained by means of functional calculus in the Banach algebra of linear bounded operators.
Keywords: fractional differential equation, Sobolev system of equations, Oskolkov system of equations, initial boundary value problem. 
@article{IIGUM_2015_12_a1,
     author = {D. M. Gordievskikh and V. E. Fedorov},
     title = {Solutions for initial boundary value problems for some degenerate equations systems of fractional order with respect to the time},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {12--22},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a1/}
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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. The Bulletin of Irkutsk State University. Series Mathematics, Tome 12 (2015), pp. 12-22. http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a1/