Abstract—In this paper, we study a system of nonlinear Riemann-Liouville fractional ordinary differential equations with parameters, subject to coupled multi-point boundary conditions which contain fractional derivatives. By using some properties of the associated Green's functions and the Guo-Krasnosel’skii fixed point theorem, we prove the existence of positive solutions for this problem when the parameters belong to various intervals. Then, we present sufficient conditions for the nonexistence of positive solutions.

Index Terms—Fractional differential equations, multi-point boundary conditions, positive solutions, existence, nonexistence.

Johnny Henderson is with Baylor University, Department of Mathematics, Waco, Texas, 76798-7328 USA.
Rodica Luca is with Gh. Asachi Technical University, Department of Mathematics, Iasi 700506, Romania (email: rluca@math.tuiasi.ro rlucatudor@yahoo.com).
Alexandru Tudorache is with Gh. Asachi Technical University, Faculty of Computer Engineering and Automatic Control, Iasi 700050, Romania.

Cite: Johnny Henderson, Rodica Luca, Alexandru Tudorache, "Positive Solutions for a System of Fractional Differential Equations with Parameters and Coupled Multi-point Boundary Conditions," International Journal of Applied Physics and Mathematics vol. 8, no. 4, pp. 53-65, 2018.