Title: Positive Solutions for Multi-Order Nonlinear Fractional Systems
Author(s): A. Guezane-Lakoud, R. Khaldi
Pages: 18-22
Cite as:
A. Guezane-Lakoud, R. Khaldi, Positive Solutions for Multi-Order Nonlinear Fractional Systems, Int. J. Anal. Appl., 15 (1) (2017), 18-22.


In this paper, we study the existence of positive solutions for a class of multi-order systems of fractional differential equations with nonlocal conditions. The main tool used is Schauder fixed point theorem and upper and lower solutions method. The results obtained are illustrated by a numerical example.

Full Text: PDF



  1. B. Ahmad, A. Alsaedi, Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations. Fixed Point Theory Appl. 2010 (2010), Art. ID 364560. Google Scholar

  2. B. Ahmad, Juan J. Nieto, Riemann–Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound Value Probl. 2011 (2011), Art. ID 36. Google Scholar

  3. Y. Chai, L. Chen, R. Wu, Inverse projective synchronization between two different hyperchaotic systems with fractional order. J. Appl. Math. 2012 (2012), Article ID 762807. Google Scholar

  4. M. Feng, X. Zhang, W. Ge, New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions . Bound. Value Probl. 2011 (2011), Art. ID 720702. Google Scholar

  5. A. Guezane-Lakoud, A. Ashyralyev, Positive Solutions for a System of Fractional Differential Equations with Nonlocal Integral Boundary Conditions. Differ. Equ. Dyn. Syst., DOI: 10.1007/s12591-015-0255-9. Google Scholar

  6. J. Henderson, S. K. Ntouyas, I.K. Purnaras, Positive solutions for systems of generalized three-point nonlinear boundary value problems. Comment. Math. Univ. Carolin. 49 (2008), 79-91. Google Scholar

  7. R. Khaldi, A. Guezane-Lakoud, Upper and lower solutions method for higher order boundary value problems, Progress in Fractional Differentiation and Applications, Progr. Fract. Differ. Appl. 3 (1) (2017), 53-57. Google Scholar

  8. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam 2006. Google Scholar

  9. S. K. Ntouyas, M. Obaid, A coupled system of fractional differential equations with nonlocal integral boundary conditions. Adv. Differ. Equ. 2012 (2012), Article ID 130. Google Scholar

  10. I. Podlubny, Fractional Differential Equations Mathematics in Sciences and Engineering. Academic Press, New York 1999. Google Scholar

  11. M. Rehman, R. Khan, A note on boundary value problems for a coupled system of fractional differential equations. Comput. Math. Appl. 61 (2011), 2630-2637. Google Scholar


Copyright © 2020 IJAA, unless otherwise stated.