# Existence of Positive Solutions for a Coupled System of (p, q)-Laplacian Fractional Higher Order Boundary Value Problems

## Main Article Content

### Abstract

In this paper, we establish the existence of at least three positive solutions for a system of (p,q)-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach space.

## Article Details

### References

- R. P. Agarwal, D. O'Regan and P. J. Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
- D. R. Anderson and J. M. Davis, Multiple positive solutions and eigenvalues for third order right focal boundary value problems, J. Math. Anal. Appl., 267(2002), 135-157.
- R. I. Avery, A generalization of the Leggett-Williams fixed point theorem, Math. Sci. Res. Hot-line, 3(1999), 9-14.
- R. I. Avery and J. Henderson, Existence of three positive pseudo-symmetric solutions for a onedimensional p-Laplacian, J. Math. Anal. Appl., 277(2003), 395-404.
- C. Bai, Existence of positive solutions for boundary value problems of fractional functional differential equations, Elec. J. Qual. Theory Diff. Equ., 30(2010), 1-14.
- Z. Bai and H. L ¨u, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311(2005), 495-505.
- G. Chai, Positive solutions for boundary value problem of fractional differential equation with pLaplacian operator, Bound. Value Probl., 2012(2012), 1-18.
- T. Chen and W. Liu, An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator, Appl. Math. Lett., 25(2012), 1671-1675.
- R. Dehghani and K. Ghanbari, Triple positive solutions for boundary value problem of a nonlinear fractional differential equation, Bulletin of the Iranian Mathematical Society, 33(2007), 1-14.
- L. Diening, P. Lindqvist and B. Kawohl, Mini-Workshop: The p-Laplacian Operator and Applications, Oberwolfach Reports, 10(2013) 433-482.
- L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120(1994), 743-748.
- C. Goodrich, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl., 62(2011), 1251-1268.
- D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Acadamic Press, San Diego, 1988.
- J. Henderson and S. K. Ntouyas, Positive solutions for systems of nonlinear boundary value problems, Nonlinear Stud., 15(2008), 51-60.
- A. A. Kilbas, H. M. Srivasthava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science, Amsterdam, 2006.
- L. Kong and J. Wang, Multiple positive solutions for the one-dimensional p-Laplacian, Nonlinear Anal., 42(2000), 1327-1333.
- I. Podulbny, Fractional Diffrential Equations, Academic Press, San Diego, 1999.
- K. R. Prasad and B. M. B. Krushna, Multiple positive solutions for a coupled system of p-Laplacian fractional order two-point boundary value problems, Int. J. Differ. Equ., 2014(2014), Article ID 485647, 1-10.
- K. R. Prasad and B. M. B. Krushna, Multiple positive solutions for the system of (n, p)-type fractional order boundary value problems, Bull. Int. Math. Virtual Inst., 5(2015), 1-12.
- K. R. Prasad and B. M. B. Krushna, Solvability of p-Laplacian fractional higher order two-point boundary value problems, Commun. Appl. Anal., 19(2015), 659-678.
- X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett., 22(2009), 64-69.
- C. Yang, J. Yan, Positive solutions for third order Sturm-Liouville boundary value problems with p-Laplacian, Comput. Math. Appl., 59(2010), 2059-2066.