tailieunhanh - Báo cáo hóa học: " Boundedness and Lagrange stability of fractional order perturbed system related to unperturbed systems with initial time difference in Caputo’s sense"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Boundedness and Lagrange stability of fractional order perturbed system related to unperturbed systems with initial time difference in Caputo’s sense | Yakar et al. Advances in Difference Equations 2011 2011 54 http content 2011 1 54 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Boundedness and Lagrange stability of fractional order perturbed system related to unperturbed systems with initial time difference in Caputo s sense Coậkun Yakar1 Muhammed Ọpek1 and Mustafa Bayram Gucen2 Correspondence cyakar@gyte. department of Mathematics Gebze Institute of Technology Gebze-Kocaeli 141-41400 Turkey Full list of author information is available at the end of the article Springer Abstract In this paper we have investigated that initial time difference boundedness criteria and Lagrange stability for fractional order differential equation in Caputo s sense are unified with Lyapunov-like functions to establish comparison result. The qualitative behavior of a perturbed fractional order differential equation with Caputo s derivative that differs in initial position and initial time with respect to the unperturbed fractional order differential equation with Caputo s derivative has been investigated. We present a comparison result that again gives the null solution a central role in the comparison fractional order differential equation when establishing initial time difference boundedness criteria and Lagrange stability of the perturbed fractional order differential equation with respect to the unperturbed fractional order differential equation in Caputo s sense. AMS MOS Subject Classification 34C11 34D10 34D99. Keywords initial time difference ITD boundedness and Lagrange stability fractional order differential equation perturbed fractional order differential systems comparison results 1 Introduction The concept of noninteger-order derivative popularly known as fractional derivative goes back to the 17th century 1 2 . It is only a few decades ago it was realized that the derivatives of arbitrary order provide an excellent framework for modeling the .