Abstract
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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.
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Ilolov, M.I. Fractional Linear Volterra Integro-Differential Equations in Banach Spaces. J Math Sci 268, 56–62 (2022). https://doi.org/10.1007/s10958-022-06179-y
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DOI: https://doi.org/10.1007/s10958-022-06179-y
Keywords and phrases
- Caputo fractional derivative
- fractional resolvent
- Volterra integro-differential equation
- Mittag-Leffler function
- Hille–Yosida theorem
- fractional resolvent equation