TAILIEUCHUNG - Báo cáo sinh học: " Research Article New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 720702 20 pages doi 2011 720702 Research Article New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions Meiqiang Feng 1 Xuemei Zhang 2 3 and WeiGao Ge3 1 School of Applied Science Beijing Information Science Technology University Beijing 100192 China 2 Department of Mathematics and Physics North China Electric Power University Beijing 102206 China 3 Department of Mathematics Beijing Institute of Technology Beijing 100081 China Correspondence should be addressed to Meiqiang Feng meiqiangfeng@ Received 16 March 2010 Revised 24 May 2010 Accepted 5 July 2010 Academic Editor Feliz Manuel Minhos Copyright 2011 Meiqiang Feng et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. This paper investigates the existence and multiplicity of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions. The results are established by converting the problem into an equivalent integral equation and applying Krasnoselskii s fixed-point theorem in cones. The nonexistence of positive solutions is also studied. 1. Introduction Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modelling of systems and processes in the fields of physics chemistry aerodynamics electrodynamics of complex medium polymer rheology Bode s analysis of feedback amplifiers capacitor theory electrical circuits electron-analytical chemistry biology control theory fitting of experimental data and so forth and involves derivatives of fractional order. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and .

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