Geodesic
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. 
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     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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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/