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Stability analysis of the fractional differential systems with Miller-Ross sequential derivative

QIAN De-liang1 LI Chang-pin2(1.College of Science;Zhongyuan University;Henan 450007;China 2.Department of Mathematics;Shanghai University;Shanghai 200444;China)

  Because of lacking of the semigroup property of Riemann-Liouville derivative and Caputo one,the Miller-Rose sequential fractional derivative operator,which in the sense of this two types of fractional derivatives,has been proposed,which often appears in a nature way in the formulation of various applied problems in physics and applied sciences.In this paper,by using the Laplace transform,the solutions of the systems with the Miller-Ross sequential derivative in the sense of the Riemann-Liouville derivative and the Caputo one are derived respectively.Basing on the asymptotical expansion of the Mittag-Leffler function,the stability criteria of the fractional differential systems with Miller-Ross sequential fractional derivative are given,where two cases are included:the homogenous case and the non-homogenous one.……