The (integer order) Halanay inequality with distributed delays is extended to the fractional order case. It is proved that solutions decay to zero as a Mittag-Leffler function as time goes to infinity provided that th...The (integer order) Halanay inequality with distributed delays is extended to the fractional order case. It is proved that solutions decay to zero as a Mittag-Leffler function as time goes to infinity provided that the delay feedback are bounded by similar functions.An application to a problem arising in neural network theory is provided showing that the equilibrium is Mittag-Leffler stable.展开更多
基金supported by National Natural Science Foundation of the People’s Republic of China(61963033)the Key Project of Natural Science Foundation of Xinjiang(2021D01D10)。
基金Supported by King Abdulaziz City of King Abdulaziz City of Science and Technology (KACST) under the National Science,Technology and Innovation Plan(NSTIP),Project No.15-OIL4884-0124
文摘The (integer order) Halanay inequality with distributed delays is extended to the fractional order case. It is proved that solutions decay to zero as a Mittag-Leffler function as time goes to infinity provided that the delay feedback are bounded by similar functions.An application to a problem arising in neural network theory is provided showing that the equilibrium is Mittag-Leffler stable.
基金supported by The National Natural Science Foundation of P.R. China (60764003)The Major Project of The Ministry of Education of P.R. China (207130)The Scientific Research Programmes of Colleges in Xinjiang (XJEDU2007G01, XJEDU2006I05)
基金The National Natural Science Foundation of China(11201038)the Youth Science and Technology Nova Program of Shaanxi Province(2014KJXX-55)the Special Fund for Basic Scientific Research of Central Colleges in Chang’an University(2013G2121017)
