Solvability analysis of a special type fractional differential system

Obtained some new and original results in investigation of solutions of the boundary-value problems (BVPs) for fractional differential systems (FDS), subjected to anti-periodic boundary conditions. The approximate solution of the given BVP is built in the form of successive sequences of functions by using main ideas of the numerical–analytic technique (Marynets in Electron J Qual Theory Differ Equ 6(2016):1–14 (2016); Ronto and Marynets in Nonlinear Oscil 14:379–413 (2012), Ronto et al. in Tatra Mt Math Publ 63:247–267 (2015). The numerical values of the unknown vector-parameter are solutions of the so-called 'determining' system of algebraic or transcendental equations.