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: Research Article Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 364560 17 pages doi 2010 364560 Research Article Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations Bashir Ahmad and Ahmed Alsaedi Department of Mathematics Faculty of Science King Abdulaziz University 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Bashir Ahmad bashir_qau@ Received 14 May 2010 Accepted 11 August 2010 Academic Editor Juan J. Nieto Copyright 2010 B. Ahmad and A. Alsaedi. 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 study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented. 1. Introduction In recent years the applications of fractional calculus in physics chemistry electrochemistry bioengineering biophysics electrodynamics of complex medium polymer rheology aerodynamics continuum mechanics signal processing electromagnetics and so forth are highlighted in the literature. The methods of fractional calculus when .
