| Autors: Madamlieva, E. B., Milev, M., Stoyanova, T. Title: On Stability Criteria Induced by the Resolvent Kernel for a Fractional Neutral Linear System with Distributed Delays Keywords: fractional derivatives; neutral fractional systems; distribu Abstract: We consider an initial problem (IP) for a linear neutral system with distributed delays and derivatives in Caputo’s sense of incommensurate order, with different kinds of initial functions. In the case when the initial functions are with bounded variation, it is proven that this IP has a unique solution. The Krasnoselskii’s fixed point theorem, a very appropriate tool, is used to prove the existence of solutions in the case of the neutral systems. As a corollary of this result, we obtain the existence and uniqueness of a fundamental matrix for the homogeneous system. In the general case, without additional assumptions of boundedness type, it is established that the existence and uniqueness of a fundamental matrix lead existence and uniqueness of a resolvent kernel and vice versa. Furthermore, an explicit formula describing the relationship between the fundamental matrix and the resolvent kernel is proven in the general case too. On the base of the existence and uniqueness of a resolve References Issue
|
Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus
