, Volume 58, Issue 2, pp 359–369

Multiple positive solutions for fractional differential systems

Open Access


In this paper, we study the existence of positive solution to boundary value problem for fractional differential system
$$\left\{\begin{array}{ll}D_{0^+}^\alpha u (t) + a_1 (t) f_1 (t, u (t), v (t)) = 0,\;\;\;\;\;\;\;\quad t \in (0, 1),\\D_{0^+}^\alpha v (t) + a_2 (t) f_2 (t, u (t), v (t)) = 0,\;\;\;\;\;\;\;\quad t \in (0, 1), \;\; 2 < \alpha < 3,\\u (0)= u' (0) = 0, \;\;\;\; u' (1) - \mu_1 u' (\eta_1) = 0,\\v (0)= v' (0) = 0, \;\;\;\; v' (1) - \mu_2 v' (\eta_2) = 0,\end{array}\right.$$
where \({D_{0^+}^\alpha}\) is the Riemann-Liouville fractional derivative of order α. By using the Leggett-Williams fixed point theorem in a cone, the existence of three positive solutions for nonlinear singular boundary value problems is obtained.


Cone Multi point boundary value problem Fixed point theorem Riemann-Liouville fractional derivative 

Mathematical Subject Classification

47H10 26A33 34A08 


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesRazi UniversityKermanshahIran

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