Positive Solutions for a Singular Sum Fractional Differential System

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Mehdi Shabibi
Mihai Postolache
Shahram Rezapour

Abstract

We investigate the existence of positive solutions for a singular sum fractional differential system under some boundary conditions by providing different conditions. Also, we give an example to illustrate one of our main results.

Article Details

References

  1. R. P. Agarwal, D. O'Regan and S. Stanek, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. Math. Anal. Appl. 371 (2010), 57-68.
  2. R. P. Agarwal, D. O'Regan and S. Stanek, Positive solutions for mixed problems of singular fractional differential equations, Math. Nachr. 285 (1) (2012), 27-41.
  3. Z. Bai and T. Qiu, Existence of positive solution for singular fractional differential equation, Appl. Math. Comput. 215 (2009), 2761-2767.
  4. Z. Bai, W. Sun and W. Zhang, Positive solutions for boundary value problems of singular fractional differential equations, Abstr. Appl. Anal. 2013 (2013), Art. ID 129640.
  5. I. Podlubny, Fractional Differential Equations, Academic Press, 1999.
  6. R. Li, H. Zhang and H. Tao, Unique solution of a coupled fractional differential system involving integral boundary conditions from economic model, Abstr. Appl. Anal. 2013 (2013), Art. ID 615707.
  7. Sh. Rezapour and M. Shabibi, A singular fractional fractional differential equation with Riemann-Liouville integral boundary condition, J. Adv. Math. Stud. 8 (1) (2015), 80-88.
  8. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integral and Derivative: Theory and Applications, Gordon and Breach (1993).
  9. D. R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.
  10. S. Stanek, The existence of positive solutions of singular fractional boundary value problems, Comput. Math. Appl. 62 (2011), 1379-1388.
  11. N. Tatar, An impulsive nonlinear singular version of the Gronwall-Bihari inequality, J. Inequal. Appl. 2006 (2006), Art. ID 84561.
  12. A. Yang and W. Ge, Positive solutions for boundary value problems of n-dimension nonlinear fractional differential system, Bound. Value Probl. 2008 (2008), Art. ID 437453.