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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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/

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