# Applying Lienard–Schipar’s method to solving of homogeneous fractional differential Euler-type equations on an interval

• Zhukovskaya Natalia V., wwugazi@gmail.com Belarusian State University 4 Nezavisimost’ Avenue, Minsk 220030, Belarus
• Sitnik Sergey M., sitnik@bsu.edu.ru Belgorod State National Research University, 85 Pobeda st., Belgorod 308015, Russia
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

### Abstract

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.

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How to Cite
Zhukovskaya, N. and Sitnik, S. (&nbsp;) “Applying Lienard–Schipar’s method to solving of homogeneous fractional differential Euler-type equations on an interval”, Mathematical notes of NEFU, 25(3), pp. 33-42. doi: https://doi.org/10.25587/SVFU.2018.99.16949.
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Mathematics