Geodesic
On solvability of some classes of equations with Hilfer derivative in Banach spaces
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 11-19

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The issues of unique solvability of a Cauchy-type problem for an evolutionary equation in a Banach space with a Hilfer fractional derivative and with a bounded operator are investigated. The existence of a unique solution to the problem is proved, the solution is presented using Mittag-Leffler operator functions. The abstract result is used when considering a class of initial boundary value problems for partial differential equations
Keywords: Hilfer derivative, fractional order equation, initial problem, theorem on the existence and uniqueness of a solution, linear inhomogeneous equation, initial boundary value problem, Laplace operator. 
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     title = {On solvability of some classes of equations with  {Hilfer} derivative in {Banach} spaces},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {11--19},
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     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_1_a1/}
}
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A. R. Volkova; V. E. Fedorov; D. M. Gordievskikh. On solvability of some classes of equations with  Hilfer derivative in Banach spaces. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 11-19. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_1_a1/