Abstract
This paper is concerned with the asymptotic stability of linear fractional-order neutral delay differential–algebraic systems described by the Caputo–Fabrizio (CF) fractional derivative. A novel characteristic equation is derived using the Laplace transform. Based on an algebraic approach, stability criteria are established. The effect of the index on such criteria is analyzed to ensure the asymptotic stability of the system. It is shown that asymptotic stability is ensured for the index-1 problems provided that a stability criterion holds for any delay parameter. Also, asymptotic stability is still valid for higher-index problems under the conditions that the system matrices have common eigenvectors and each pair of such matrices is simultaneously triangularizable so that a stability criterion holds for any delay parameter. An example is provided to demonstrate the effectiveness and applicability of the theoretical results.
Highlights
1 Introduction Fractional calculus is attracting more and more researchers in applied sciences and engineering because of the many advantages of fractional derivatives which provide important tools in mathematical modeling related to many interdisciplinary areas, see, e.g., [20,21,22,23,24,25,26,27,28, 34, 40]
5 Conclusions Asymptotic stability of linear fractional-order neutral delay differential–algebraic systems described by the Caputo–Fabrizio (CF) fractional derivative has been investigated
Using the Laplace transform, we have derived a new characteristic equation. This characteristic equation involves a transcendental term, which makes it difficult to use in practice and in particular to study the asymptotic stability of such a system
Summary
Fractional calculus is attracting more and more researchers in applied sciences and engineering because of the many advantages of fractional derivatives which provide important tools in mathematical modeling related to many interdisciplinary areas, see, e.g., [20,21,22,23,24,25,26,27,28, 34, 40]. It should be pointed out that fractional calculus has gained the popularity due to its peculiar properties and recent progress of research in this area. There are different types of fractional derivatives, those of Riemann–Liouville and Caputo are the most popular in the literature [4, 19, 32, 37, 39]
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