Existence of Solutions for Nonlocal Boundary Value Problems of Nonlinear Fractional Differential Equations
نویسندگان
چکیده
This paper investigates the existence of solutions of the nonlinear fractional differential equation { Du(t) + f(t, u(t),Du(t)) = 0, 0 < t < 1, 3 < α ≤ 4, u(0) = u′(0) = u′′(0) = 0, u(1) = u(ξ), 0 < ξ < 1, where D is the Caputo fractional derivative, β > 0, α− β ≥ 1. The peculiarity of this equation is that the nonlinear term depends on the fractional derivative of the unknown function, compared with the available results in literature. The equation is firstly converted to an equivalent integral equation of Fredholm type, then results for the existence of its solution are derived by means of Schauder’s fixed-point theorem. An example is given for demonstration. AMS Subject Classifications: 34B10, 34B27.
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