Geodesic
Cauchy problem for the system of equations with partial derivatives of fractional order
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 76-82

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For a system of first-order equations with partial derivatives of fractional order in the Riemann-Liouville sense, we give a correct statement of the Cauchy problem in the case when the matrix coefficient in the main part has only positive eigenvalues.
Keywords: system of partial differential equations, fractional derivatives, Cauchy problem, well-posedness, fundamental solution, Wright’s function of the matrix argument. 
@article{VKAM_2018_3_a8,
     author = {M. O. Mamchuev},
     title = {Cauchy problem for the system of equations with partial derivatives of fractional order},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {76--82},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_3_a8/}
}
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M. O. Mamchuev. Cauchy problem for the system of equations with partial derivatives of fractional order. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 76-82. http://geodesic.mathdoc.fr/item/VKAM_2018_3_a8/