مشخصات پژوهش

By using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem cDαu(t) = f (t, u(t), u(t), cDβu(t)), u(0) = au(1), u(0) = b cDβu(1), u(0) = u(0) = u(n–1)(0) = 0, where n ≥ 3 is an integer, α ∈ (n – 1, n), 0 < β < 1, 0 < a < 1, 0 < b < (2 – β), f is an Lq-Caratheodory function, q > 1 α–1 and f (t, x, y, z) may be singular at value 0 in one dimension of its space variables x, y, z. Here, cD stands for the Caputo fractional derivative.