Autors: Kiskinov, H., Madamlieva, E. B., Zahariev, A.
Title: Hyers–Ulam and Hyers–Ulam–Rassias stability for Linear Fractional Systems with Riemann–Liouville Derivatives and Distributed Delays
Keywords: Riemann–Liouville fractional derivative; distributed delay;

Abstract: The aim of the present paper is to study the asymptotic properties of the solutions of linear fractional system with Riemann–Liouville-type derivatives and distributed delays. We prove under natural assumptions (similar to those used in the case when the derivatives are first (integer) order) the existence and uniqueness of the solutions in the initial problem for these systems with discontinuous initial functions. As a consequence, we also prove the existence of a unique fundamental matrix for the homogeneous system, which allows us to establish an integral representation of the solutions to the initial problem for the corresponding inhomogeneous system. Then, we introduce for the studied systems a concept for Hyers–Ulam in time stability and Hyers–Ulam–Rassias in time stability. As an application of the obtained results, we propose a new approach (instead of the standard fixed point approach) based on the obtained integral representation and establish sufficient conditions, which gu

References

    Issue

    , 2023, Switzerland, DOI 10.3390/axioms12070637

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