Investigation of optimal control problem for single and double integrators of fractional order using the method of moments in case when admissible control belongs to $L_p[0,T]$ space

The optimal control problem investigated for two dynamical systems of fractional order (single and double integrators) in case when admissible control search evaluated in space of functions which are $p$-integrable on the segment. The problem reduced to the problem of moments. For the latter problem conditions of statement and solvability are derived. In case of $p=2$ an obvious solutions for optimal control problem are obtained. Dependencies of control norm and minimal transition time from order of fractional derivative are investigated. Comparative analysis of results for both of considered systems are evaluated.