Article

ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 58, Issue 2, pp 359-369

Open Access This content is freely available online to anyone, anywhere at any time.

Multiple positive solutions for fractional differential systems

  • Nemat NyamoradiAffiliated withDepartment of Mathematics, Faculty of Sciences, Razi University Email author 

Abstract

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.

Keywords

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

Mathematical Subject Classification

47H10 26A33 34A08