tailieunhanh - Báo cáo hóa học: " Stability of a nonlinear non-autonomous fractional order systems with different delays and non-local conditions"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :Stability of a nonlinear non-autonomous fractional order systems with different delays and non-local conditions | El-Sayed and Gaafar Advances in Difference Equations 2011 2011 47 http content 2011 1 47 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Stability of a nonlinear non-autonomous fractional order systems with different delays and non-local conditions Ahmed El-Sayed 1 and Fatma Gaafar2 Correspondence amasayed5@ 1Faculty of Science Alexandria University Alexandria Egypt Full list of author information is available at the end of the article Springer Abstract In this paper we establish sufficient conditions for the existence of a unique solution for a class of nonlinear non-autonomous system of Riemann-Liouville fractional differential systems with different constant delays and non-local condition is. The stability of the solution will be proved. As an application we also give some examples to demonstrate our results. Keywords Riemann-Liouville derivatives nonlocal non-autonomous system timedelay system stability analysis 1 Introduction Here we consider the nonlinear non-local problem of the form Dax t fi t xx t . x t gift Xi t - rx . Xn t - r t e 0 T T X 1 x t t for t 0 and lim t 0 2 t -0 I1-a x t t 0 0 3 where Da denotes the Riemann-Liouville fractional derivative of order a e 0 1 x t x1 t x2 t . xn t where denote the transpose of the matrix and fi gi 0 T X Rn R are continuous functions F t ji t n X 1 are given matrix and O is the zero matrix rj 0 j 1 2 . n are constant delays. Recently much attention has been paid to the existence of solution for fractional differential equations because they have applications in various fields of science and engineering. We can describe many physical and chemical processes biological systems etc. by fractional differential equations see 1-9 and references therein . In this work we discuss the existence uniqueness and uniform of the solution of stability non-local problem 1 - 3 . Furthermore as an application we give some examples to demonstrate our results.