Geodesic
Generalized boundary problem for an ordinary differential equation of fractional order
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 20-29

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For an ordinary differential equation of fractional order, a problem with general conditions is formulated and solved. A representation of a solution of the problem under study is found. The uniqueness theorem of a solution is proved. The boundary conditions are given in the form of linear functionals, which allows us to cover a fairly wide class of linear local and non-local conditions.
Keywords: fractional order equation, functional, Gerasimov — Caputo fractional derivative, Mittag-Leffler function. 
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     author = {L. Kh. Gadzova},
     title = {Generalized boundary problem for an ordinary differential equation of fractional order},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {20--29},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_1_a2/}
}
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L. Kh. Gadzova. Generalized boundary problem for an ordinary differential equation of fractional order. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 20-29. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_1_a2/