Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order

@article{Hao2014ApplicationOS,
  title={Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order},
  author={Mengru Hao and Chengbo Zhai},
  journal={The Journal of Nonlinear Sciences and Applications},
  year={2014},
  volume={07},
  pages={131-137}
}
  • M. Hao, C. Zhai
  • Published 6 April 2014
  • Mathematics
  • The Journal of Nonlinear Sciences and Applications
In this paper, by using Schauder xed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by D 1 0+y1(t) = 1a1(t)f(t;y1(t);y2(t)) +e1(t); D 2 0+y2(t) = 2a2(t)g(t;y1(t);y2(t)) +e2(t); where 1; 22 (n 1;n] for n > 3 and n2 N, subject to the boundary conditions y (i) 1 (0) = 0 = y (i) 2 (0), for 0 i n 2, and [D 0+y1(t)]t=1 = 0 = [D 0+y2(t)]t=1, for 1 n 2. 
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