Geodesic
An initial problem for a class of weakly degenerate semilinear equations with lower order fractional derivatives
The Bulletin of Irkutsk State University. Series Mathematics, Tome 35 (2021), pp. 34-48

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An initial value problem is studied for a class of evolutionary equations with a weak degeneration, which are nonlinear with respect to lower order fractional Gerasimov – Caputo derivatives. The linear part of the equations contains a respectively bounded pair of operators. Unique local solvability is proved in the case of a nonlinear operator depending on elements of the degeneration space only. Examples of an equation and a system of partial differential equations are given, the initial-boundary value problems for which are reduced to the initial problem for an equation in a Banach space of the studied class.
Keywords: fractional Gerasimov – Caputo derivative, fractional order differential equation, degenerate evolution equation, semilinear equation. 
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     author = {G. D. Baybulatova and M. V. Plekhanova},
     title = {An initial problem for a class of weakly degenerate semilinear equations with lower order fractional derivatives},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {34--48},
     publisher = {mathdoc},
     volume = {35},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_35_a2/}
}
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G. D. Baybulatova; M. V. Plekhanova. An initial problem for a class of weakly degenerate semilinear equations with lower order fractional derivatives. The Bulletin of Irkutsk State University. Series Mathematics, Tome 35 (2021), pp. 34-48. http://geodesic.mathdoc.fr/item/IIGUM_2021_35_a2/