Geodesic
Mixed boundary value problem for an ordinary differential equation with fractional derivatives with different origins
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 36 (2021) no. 3, pp. 65-71

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A mixed boundary value problem is solved for an ordinary differential equation containing a composition of left- and right-sided Riemann-Liouville and Caputo fractional differentiation operators. The problem is equivalently reduced to a Fredholm integral equation of the second kind, for which a sufficient condition for unique solvability is found. As a consequence, the Lyapunov inequality is proved for the problem under study.
Keywords: fractional differential equation with different origins, mixed boundary value problem, Riemann-Liouville derivative, Caputo derivative. 
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     author = {L.M. Eneeva},
     title = {Mixed boundary value problem for an ordinary differential equation with fractional derivatives with different origins},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {65--71},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2021_36_3_a4/}
}
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L.M. Eneeva. Mixed boundary value problem for an ordinary differential equation with fractional derivatives with different origins. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 36 (2021) no. 3, pp. 65-71. http://geodesic.mathdoc.fr/item/VKAM_2021_36_3_a4/