doi: 10.17706/ijapm.2018.8.4.53-65
Positive Solutions for a System of Fractional Differential Equations with Parameters and Coupled Multi-point Boundary Conditions
,
Rodica Luca
2
,
- 1 Baylor University, Department of Mathematics, Waco, Texas, 76798-7328 USA.
- 2 Gh. Asachi Technical University, Department of Mathematics, Iasi 700506, Romania
- 3 Gh. Asachi Technical University, Faculty of Computer Engineering and Automatic Control, Iasi 700050, Romania.
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.
Keywords
- Fractional differential equations
- multi-point boundary conditions
- positive solutions
- existence
- nonexistence
How to Cite
Johnny Henderson, Rodica Luca, and 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. https://doi.org/ 10.17706/ijapm.2018.8.4.53-65
Copyright & License
Copyright © 2018 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).