Geodesic
Singular integro-differential equations of the special type in Banach spaces and it’s applications
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 4, pp. 128-137

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In this paper Cauchy problem for singular integro-differential equation of the special type in Banach spaces is investigated with help of the theory of fundamental operator-functions. The corresponding fundamental operator-function is constructed, the conditions for equal generalized with classical solution are describet. The abstract results are illustrated by examples of the initial-bounbary problems of the mathematical theory of viscoelasticity.
Keywords: Banach spaces; generalized function; Jordan set; Fredholm operator; fundamental operator-function. 
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     author = {M. V. Falaleev},
     title = {Singular integro-differential equations of the special type in {Banach} spaces and it{\textquoteright}s applications},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {128--137},
     publisher = {mathdoc},
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     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2013_6_4_a8/}
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M. V. Falaleev. Singular integro-differential equations of the special type in Banach spaces and it’s applications. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 4, pp. 128-137. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_4_a8/