Solution of an oscillatory system with fractional derivative including to equations of motion and to nonlocal boundary conditions

Abstract

In the paper an oscillatory system with liquid dampers is considered, where the fractional derivative (p/q) including both equation of motion and the corresponding nonlocal boundary condition with a regular fraction step (1/q). Based on Mittag-Leffler function, an independent solution of the homogeneous equation is constructed, and on the basis of this, the formula for the solution of the corresponding boundary value problem is given. The results are illustrated by the example of periodic boundary value problems.