THE EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT BOUNDARY CONDITIONS.

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contraction mapping principle, two existence results are obtained for the following system {D0+αx(t) = f (t, y(t), D0+py(t)), t ∈ (0, 1), {D0+βy(t) = g (t, x(t), D0+qx(t)), t ∈ (0, 1), {x(0) = x'(0) = x''(0) = ⋯ = x(m-2)(0) = 0, x(1) = λx(ξ), {y(0) = y'(0) = y''(0) = ⋯ = y(m-2)(0) = 0, y(1) = λy(ξ), where 0 < ξ < 1, m ∈ N; m ≥ 2, α, β ∈ (m-1, m) and α, β, p, q, λ satisfy certain conditions. [ABSTRACT FROM AUTHOR]