Application of Lienar−Shipar method to solving of homogeneous fractional differential Euler-type equations on the half axis

Author(s):  N.V. Zhukovskaya, Belarusian State University, Minsk, Republic of Belarus, nataliazhukouskaya@gmail.com

Issue:  Volume 50, № 2

Rubric:  Mathematics

Annotation:  In the article the solution to the homogeneous fractional differential Euler-type equation on the half-axis is given in the class of functions representable by the fractional integral of order  with the density of 1L (1;) . Using method of Hermitian forms (Lienar−Shipar method) solvability conditions for the cases of two, three and a finite number of derivatives are obtained. It is shown that in the case when the characteristic equation has multiple roots, original equation admits 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, Lienar−Shipar method.

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