Geodesic
Applying Lienard–Schipar's method to solving of homogeneous fractional differential Euler-type equations on an interval
Matematičeskie zametki SVFU, Tome 25 (2018) no. 3, pp. 33-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present the solution of the homogeneous fractional differential Euler-type equation on the half-axis in the class of functions representable by the fractional integral of order $\alpha$ with the density of $L_1(0;1)$. Using the method of Hermitian forms (Lienard–Schipar's method), solvability conditions are obtained for the cases of two, three and a finite number of derivatives. It is shown that in the case when the characteristic equation has multiple roots original equation admits a solution with logarithmic singularities.
Keywords: fractional differential Euler-type equation, Riemann–Liouville fractional integral, Riemann–Liouville fractional derivative, method of Hermitian forms, Hermite's theorem, Lienard–Schipar's method. 
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     author = {N. V. Zhukovskaya and S. M. Sitnik},
     title = {Applying {Lienard{\textendash}Schipar's} method to solving of homogeneous fractional differential {Euler-type} equations on an interval},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {33--42},
     year = {2018},
     volume = {25},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2018_25_3_a2/}
}
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N. V. Zhukovskaya; S. M. Sitnik. Applying Lienard–Schipar's method to solving of homogeneous fractional differential Euler-type equations on an interval. Matematičeskie zametki SVFU, Tome 25 (2018) no. 3, pp. 33-42. http://geodesic.mathdoc.fr/item/SVFU_2018_25_3_a2/