Existence and uniqueness of solutions for a coupled system of multi-term nonlinear fractional differential equations

  • Authors:

  • Shurong Sun;Qiuping Li;Yanan Li

  • Affiliations:

  • School of Mathematics, University of Jinan, Jinan, Shandong 250022, PR China and Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA;School of Mathematics, University of Jinan, Jinan, Shandong 250022, PR China;School of Mathematics, University of Jinan, Jinan, Shandong 250022, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2012

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Abstract

In this paper, we consider an initial value problem for a coupled system of multi-term nonlinear fractional differential equations {D^@au(t)=f(t,v(t),D^@b^"^1v(t),...,D^@b^"^Nv(t)),D^@a^-^iu(0)=0,i=1,2,...,n"1,D^@sv(t)=g(t,u(t),D^@r^"^1u(t),...,D^@r^"^Nu(t)),D^@s^-^jv(0)=0,j=1,2,...,n"2, where t@?(0,1], @a@b"1@b"2...@b"N0, @s@r"1@r"2...@r"N0, n"1=[@a]+1, n"2=[@s]+1 for @a,@s@?N and n"1=@a, n"2=@s for @a,@s@?N, @b"q,@r"qR are given functions. By means of Schauder fixed point theorem and Banach contraction principle, an existence result and a unique result for the solution are obtained, respectively. As an application, some examples are presented to illustrate the main results.