The present paper deals with some oscillating and asymptotic properties of the functional differential equations of the form where λ is an arbitrary positive constant and τ > 0 is a constant delay.

The aim of the present paper is to obtain an integral representation of the solution of the Cauchy problem with discontinuous and continuous initial conditions for linear fractional differential system with Caputo-type derivatives and distributed delay. The obtained results are new even in the particular case of fractional system with constant delays.

The aim of the present work is to establish explicit conditions for global asymptotic stability of neutral linear fractional differential system with distributed delays. The derivatives in the system can be of Riemann-Liouville or Caputo type. We consider basically the incommensurate case but some results are given for the commensurate case too. The proposed conditions are based on the logarithmic norm technique and part of the results are new even in the particular case of system with constant delays.

The aim of the present work is to study the initial value problem for neutral linear fractional differential system with distributed delays in incommensurate case. Furthermore, in the autonomous case with derivatives in the Riemann-Liouville or Caputo sense we establish that if all roots of the introduced characteristic equation have negative real parts, then the zero solution is globally asymptotically stable. The proposed condition coincides with the conditions which guaranty the same result in the particular case of system with constant delays.