Geodesic
Cauchy problem for ordinary differential equation with discretely distributed fractional differentiation operator
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 48-56

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We consider an initial value problem for ordinary differential equation with discretely distributed fractional differentiation operator. We give the Lagrange formula, prove the existence and uniqueness theorem and construct an explicit form of solution.
Keywords: fundamental solution, Cauchy problem, fractional differentiation operator, Caputo derivative. 
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     author = {L. Kh. Gadzova},
     title = {Cauchy problem for ordinary differential equation with discretely distributed fractional differentiation operator},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {48--56},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_3_a5/}
}
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L. Kh. Gadzova. Cauchy problem for ordinary differential equation with discretely distributed fractional differentiation operator. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 48-56. http://geodesic.mathdoc.fr/item/VKAM_2018_3_a5/