Existence results for fractional-order differential equations with nonlocal multi-point-strip conditions involving Caputo derivative

In this paper, we investigate the existence and uniqueness of solutions for a differential equation of fractional-order subject to nonlocal boundary conditions involving Caputo derivative of the form x(O) = delta x(sigma), a(c)D(mu)x(rho(1))+b(c)D(mu)x(rho(2)) = c integral(beta 2)(beta 1) (c)D(mu)x(s)ds 0 < rho(1) < sigma < beta(1) < beta(2) < rho(2) < 1,0 < mu < 1, and delta, a, b, c are real constants. We make use of some standard tools of fixed point theory to obtain the desired results which are well illustrated with the aid of examples.