ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 58, Issue 2, pp 359–369

Multiple positive solutions for fractional differential systems

Authors

    • Department of Mathematics, Faculty of SciencesRazi University
Open AccessArticle

DOI: 10.1007/s11565-012-0155-7

Cite this article as:
Nyamoradi, N. Ann Univ Ferrara (2012) 58: 359. doi:10.1007/s11565-012-0155-7

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

Copyright information

© The Author(s) 2012