Geodesic
On analytical in a sector resolving families of operators for strongly degenerate evolution equations of higher and fractional orders
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 82-96.

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In this paper, we study a class of linear evolution equations of fractional order that are degenerate on the kernel of the operator under the sign of the derivative and on its relatively generalized eigenvectors. We prove that in the case considered, in contrast to the case of first-order degenerate equations and equations of fractional order with weak degeneration (i.e., degeneration only on the kernel of the operator under the sign of the derivative), the family of analytical in a sector operators does not vanish on relative generalized eigenspaces of the operator under the sign of the derivative, has a singularity at zero, and hence does not determine any solution of a strongly degenerate equation of fractional order. For the case of a strongly degenerate equation of integer order this fact does not holds, but the behavior of the family of resolving operators at zero cannot be examined by ordinary method.
Keywords: degenerate evolution equation, differential equation of fractional order, analytical in a sector resolving family of operators, initial-boundary-value problem. 
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     author = {V. E. Fedorov and E. A. Romanova},
     title = {On analytical in a sector resolving families of operators for strongly degenerate evolution equations of higher and fractional orders},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {82--96},
     publisher = {mathdoc},
     volume = {137},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_137_a4/}
}
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V. E. Fedorov; E. A. Romanova. On analytical in a sector resolving families of operators for strongly degenerate evolution equations of higher and fractional orders. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 82-96. http://geodesic.mathdoc.fr/item/INTO_2017_137_a4/