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.

Abstract


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.

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References


  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.

  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.

  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.

  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.

  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.

  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.

  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.

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

  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.

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

  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.