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Báo cáo hóa học: " Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions"

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 www.boundaryvalueproblems.eom 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@yahoo.com department of Mathematics Faculty of Science King Abdulaziz University P.O. 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 1.1 subject to the boundary conditions of fractional order given by Da-2u 0 0 1.2 Da-1 u 0 vIa-1 u n 0 n T V is a constant 1.3 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 .