Asymptotic synchronization for Riemann-Liouville fractional-order delayed BAM neural networks by the exponential-type controllers

This paper considers the globally asymptotic synchronization (GAS) of drive-response Riemann-Liouville fractional-order BAM neural networks (DRRLFOBAMNNS). By using the integral inequality techniques, L’Hospital rule and integral mean-valued theorem, two new criteria are derived assuring the GAS for discussed DRRLFOBAMNNS under the exponential-type controllers \(e^{t^{\alpha _1}}\) $e^{t^{{\alpha }_1}}$ and \(e^{t^{\beta _1}}\) $e^{t^{{\beta }_1}}$ . The exponential-type controllers play the key role in studying GAS for the considered systems. The exponential-type controllers \(e^{t^{\alpha _1}}\) $e^{t^{{\alpha }_1}}$ and \(e^{t^{\beta _1}}\) $e^{t^{{\beta }_1}}$ designed are used to study the synchronization is a novel work. L’Hospital rule together with integral mean-valued theorem is applied to researching the synchronization for DRRLFOBAMNNS is a novel study work. Until now, the parameters in the controllers all are assumed to be negative numbers in the study of synchronization for neural networks (NNS), however, the parameters in our controllers in the paper are assumed to all be positive, which extends the valued-field of the parameters and makes the limits of the error variables be all zero when \({t\rightarrow \infty }\) $t\to \infty$ in the synchronization study work.