Autors: Madamlieva, E. B., Kiskinov, H., Petkova, M., Zahariev, A.
Title: On the Preservation with Respect to Nonlinear Perturbations of the Stability Property for Nonautonomous Linear Neutral Fractional Systems with Distributed Delays
Keywords: fractional derivatives; neutral fractional systems; distribu

Abstract: In the present paper, sufficient conditions are obtained under which the Cauchy problem for a nonlinearly perturbed nonautonomous neutral fractional system with distributed delays and Caputo type derivatives has a unique solution in the case of initial functions with first-kind discontinuities. For this system, by applying a formula for the integral presentation of the solution of the nonhomogeneous linear neutral fractional system, we found some additional natural conditions to ensure that from the global asymptotically stability of the zero solution of the linear part of the nonlinearly perturbed system, global asymptotic stability of the zero solution of the whole nonlinearly perturbed system follows.

References

    Issue

    , 2022, Switzerland, https://doi.org/10.3390/math10152642

    Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Web of Science