Geodesic
Lyapunov inequality for an equation with fractional derivatives with different origins
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 28 (2019) no. 3, pp. 32-39

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We consider an ordinary differential equation of fractional order with the composition of left and rightsided fractional derivatives, which is a model equation of motion in fractal media. We find a necessary condition for existence of nontrivial solution of homogeneous Dirichlet problem for the equation under consideration. The condition has the form of integral estimate for the potential and is an analog of Lyapunov inequality.
Keywords: Riemann-Liouville fractional derivative, Caputo fractional derivative, Dirichlet problem, Lyapunov inequality. 
@article{VKAM_2019_28_3_a3,
     author = {L M. Eneeva},
     title = {Lyapunov inequality for an equation with fractional derivatives with different origins},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {32--39},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2019_28_3_a3/}
}
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L M. Eneeva. Lyapunov inequality for an equation with fractional derivatives with different origins. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 28 (2019) no. 3, pp. 32-39. http://geodesic.mathdoc.fr/item/VKAM_2019_28_3_a3/