Fractional linear Volterra integro-differential equations in Banach spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 58-64
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The paper presents the foundations of the theory of linear fractional Volterra integro-differential equations of convolution type in Banach spaces. It is established that the existence of a fractional resolvent operator for such equations is equivalent to the well-posedness of the formulation of the initial problem for them. Within the framework of this approach, a theorem of the Hille–Yosida type is proved.
Keywords:
Caputo fractional derivative, fractional resolvent, Volterra integro-differential equation, Mittag-Leffler function, Hille–Yosida theorem, fractional resolvent equation.
@article{INTO_2019_173_a4,
author = {M. I. Ilolov},
title = {Fractional linear {Volterra} integro-differential equations in {Banach} spaces},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {58--64},
publisher = {mathdoc},
volume = {173},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2019_173_a4/}
}
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%0 Journal Article %A M. I. Ilolov %T Fractional linear Volterra integro-differential equations in Banach spaces %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2019 %P 58-64 %V 173 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2019_173_a4/ %G ru %F INTO_2019_173_a4
M. I. Ilolov. Fractional linear Volterra integro-differential equations in Banach spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 58-64. http://geodesic.mathdoc.fr/item/INTO_2019_173_a4/