APPLYING LIENARD–SCHIPAR’S METHOD TO SOLVING OF HOMOGENEOUS FRACTIONAL DIFFERENTIAL EULER–TYPE EQUATIONS ON AN INTERVAL
https://doi.org/10.25587/SVFU.2018.99.16949
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 α with the density of L1(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.
About the Authors
N. V. Zhukovskaya
Belarusian State University
Belarus
Belarus
Natalia V. Zhukovskaya
Belarusian State University, 4 Nezavisimost Avenue, Minsk 220030, Belarus
S. M. Sitnik
Belgorod State National Research University
Russian Federation
Russian Federation
Sergey M. Sitnik
Belgorod State National Research University, 85 Pobeda Street, Belgorod 308015, Russia
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Review
For citations:
Zhukovskaya N.V., Sitnik S.M. APPLYING LIENARD–SCHIPAR’S METHOD TO SOLVING OF HOMOGENEOUS FRACTIONAL DIFFERENTIAL EULER–TYPE EQUATIONS ON AN INTERVAL. Mathematical notes of NEFU. 2018;25(3):33-42. (In Russ.) https://doi.org/10.25587/SVFU.2018.99.16949
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