Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 691721 10 pages doi 2010 691721 Research Article Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions Ahmed Alsaedi and Bashir Ahmad Department of Mathematics Faculty of Science King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Bashir Ahmad bashir_qau@ Received 17 March 2010 Revised 6 May 2010 Accepted 11 June 2010 Academic Editor Kanishka Perera Copyright 2010 A. Alsaedi and B. Ahmad. 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. We prove the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q e 1 2 with three-point nonlocal fractional boundary conditions by applying some standard fixed point theorems. 1. Introduction Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics electricity chemistry biology economics control theory signal and image processing polymer rheology regular variation in thermodynamics biophysics blood flow phenomena aerodynamics electro-dynamics of complex medium viscoelasticity and damping control theory wave propagation percolation identification and fitting of experimental data 1-4 . Recently differential equations of fractional order have been addressed by several researchers with the sphere of study ranging from the theoretical aspects of existence and uniqueness of solutions to the analytic and numerical methods for finding
