Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions | Ahmad and Nieto Boundary Value Problems 2011 2011 36 http content 2011 1 36 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions Bashir Ahmad 1 and Juan J Nieto1 2 Correspondence bashir_qau@ department of Mathematics Faculty of Science King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Full list of author information is available at the end of the article Springer Abstract This article investigates a boundary value problem of Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Some new existence results are obtained by applying standard fixed point theorems. 2010 Mathematics Subject Classification 26A33 34A34 34B15. Keywords Riemann-Liouville calculus fractional integro-differential equations fractional boundary conditions fixed point theorems 1 Introduction In this article we study the existence and uniqueness of solutions for the following nonlinear fractional integro-differential equation Dau t f t u t 0u t Ỷu t t e 0 T a e 1 2 subject to the boundary conditions of fractional order given by Da-2u 0 0 Da-1 u 0 vIa-1 u n 0 n T V is a constant where Da denotes the Riemann-Liouville fractional derivative of order a f 0 T X R X R X R R is continuous and t t t frttMM W -fsMs fe 0 0 with g and Ỏ being continuous functions on 0 T X 0 T . Boundary value problems for nonlinear fractional differential equations have recently been investigated by several researchers. As a matter of fact fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes see 1 and make the fractional-order models more realistic and practical than the classical integer-order models. Fractional differential equations arise in many engineering and scientific .
