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: Fractional nonlocal impulsive quasilinear multi-delay integro-differential systems | Debbouche Advances in Difference Equations 2011 2011 5 http content 2011 1 5 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Fractional nonlocal impulsive quasilinear multi-delay integro-differential systems Amar Debbouche Correspondence amar_debbouche@ Department of Mathematics Faculty of Science Guelma University Guelma Algeria SpringerOpen0 Abstract In this article sufficient conditions for the existence result of quasilinear multi-delay integro-differential equations of fractional orders with nonlocal impulsive conditions in Banach spaces have been presented using fractional calculus resolvent operators and Banach fixed point theorem. As an application that illustrates the abstract results a nonlocal impulsive quasilinear multi-delay integro-partial differential system of fractional order is given. AMS Subject Classifications. 34K05 34G20 26A33 35A05. Keywords Fractional integrodifferential systems resolvent operators nonlocal and impulsive conditions fixed point theorem Introduction Many fractional models can be represented by the following system a t u A t u t u t f t u t u 0 t g t s u s u y s ds dta 0 u 0 h u U0 Xu ti Ii u ti in a Banach space X where 0 a 1 t e 0 a u0 e X i 1 2 . m and 0 t1 t2 tm a. We assume that -A t . is a closed linear operator defined on a dense domain D A in X into X such that D A is independent of t. It is assumed also that -A t . generates an evolution operator in the Banach space X. The functions f J Xr 1 X g A X Xk 1 X h PC J X X u b u b1 . u br u Ỳ 1 . u k and bp gq J J are given where p 1 2 . r and q 1 2 . k. Here J 0 a and A t s . 0 s t a . Let PC J X consist of functions u from J into X such that u t is continuous at t ti and left continuous at t ti and the right limit u t exists for i 1 2 . m. Clearly PC J X is a Banach space with the norm u PC supteJ u t and let Xu ti u t u t constitutes an impulsive condition. Fractional differential .
