New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays

Abstract

• A novel generalized FODGI with two different orders is developed, which includes the one in [39, Theorem 3.2] as a special case and can be used to analyze the qualitative properties of various FODSs with two different orders. • As a straightforward generalization, a novel generalized FODGI with multiple different orders is also established, which includes the one in [40, Theorem 1.4] as a special case. • Two novel FTS criteria of FOBAMNNs with the orders 0 < ℘ < 1 and 1 < ℘< 2 are established by the obtained FODGI with two different orders. In this approach, the term w ( t ) and delay term w ( t − τ ) can be analyzed in a unified framework. This is to say, the delay term w ( t − τ ) needs not to be transformed to the term w ( t ). • Comparisons with the existing contributions: a) The obtained results in this article is less conservative than the ones in the existing works [30, 31]. b) There are delay terms in the obtained novel FODGI with multiple different orders. Therefore, the proposed inequality in this article is more general. The finite-time stability (FTS) for fractional-order bidirectional associative memory neural networks (FOBAMNNs) with discrete and distributed delays is investigated in this article. Firstly, a novel fractional-order delayed Gronwall inequality (FODGI) with two different orders is developed. As a straightforward generalization, a novel generalized FODGI with multiple different orders is also established, which can be applied to investigate the stability of fractional-order delayed systems (FODSs) with multiple different orders. Secondly, based on the former inequality, two novel FTS criteria of FOBAMNNs with the orders 0 < ℘ < 1 and 1 < ℘ < 2 are established. Finally, three examples are exhibited to illustrate the effectiveness and the less conservativeness of the proposed methods.