tailieunhanh - Báo cáo hóa học: " Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders | Zhao et al. Advances in Difference Equations 2011 2011 10 http content 2011 1 10 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders Yige Zhao1 Shurong Sun1 2 Zhenlai Han1 3 and Wenquan Feng1 Correspondence sshrong@163. com 1School of Science University of Jinan Jinan 250022 Shandong PR China Full list of author information is available at the end of the article SpringerOpen0 Abstract In this article we study the existence of positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders -Da u t f t v t 0 t 1 D0 v t g t u t 0 t 1 u 0 u 1 u 0 v 0 v 1 v 0 v 1 0 where 2 a 3 3 b 4 DJ5 Dq are the standard Riemann-Liouville fractional derivative and f g 0 1 X 0 0 are given continuous functions f t 0 - 0 g t 0 - 0. Our analysis relies on fixed point theorems on cones. Some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established. As an application examples are presented to illustrate the main results. Keywords Positive solution coupled system fractional Green s function fixed point theorem 1 Introduction Fractional differential equations have been of great interest recently. It is caused by the both intensive development of the theory of fractional calculus itself and applications see 1-6 . Recently there are a large number of papers dealing with the existence of solutions of nonlinear fractional differential equations by the use of techniques of nonlinear analysis fixed point theorems Leray-Schauder theory Adomian decomposition method etc. see 7-21 . The articles 13-21 considered boundary value problems for fractional differential equations. Yu and Jiang 20 examined the existence of positive solutions for the following problem Dau t f t u t 0 0 t 1 u 0 u 1 u 0 0 where 2 a 3 is a real number f e C