Abstract
In this paper, we establish the criteria for the existence and uniqueness of solutions of a two-point BVP for a system of nonlinear fractional differential equations on time scales.
Delta a*q(1-1) x(t) = f(1)(t, x(t), y (t)), t is an element of J: = left perpendiculara, bright perndicular boolean AND T,
Delta a*q(2-1) x(t) = f(2)(t, x(t), y (t)), t is an element of J: = left perpendiculara, bright perndicular boolean AND T,
subject to the boundary conditions
x(a) = 0, x Delta(b) = 0, x(Delta Delta()b) = 0,
x(a) = 0, y Delta(b) = 0, y(Delta Delta()b) = 0,
where T is any time scale (nonempty closed subsets of the reals), 2 < alpha(i) < 3 and f(i) is an element of C-rd ([a, b] x R x R, R) and ai-1 a(i) denotes the delta fractional derivative on time scales T of order ai - 1 for i = 1, 2. By using the Banach contraction principle. Finally, an example is given to illustrate the main result.