Existence results for a semipositone singular fractional differential equation

Positive solutions for singular semipositone nonlinear fractional differential system

“…In particular, then, our results provide an immediate generalization of [4] and [15]. On the other hand, many works have studied changing-sign boundary value problems, see, [3,6,[10][11][12][13][16][17][18][19] and the refrences therein.…”

“…Here n = [α] + 1, [α] denotes the integer part of the real number α. Now, we recall the explicit expression of the Green's function for the linear fractional differential equation associated to (3) see ( [3])…”

“…Using Propsition 2.6 in [3], 0 < σ 0 q < ∞ if and only if (1 − s) α−1 q(s) ∈ C(0, 1) ∩ L(0, 1). Then by Lemma 2.4 problem ( 11)-( 12) has a unique solution (w 1 , w 2 ) with…”

“…However, in our work and under uncoupled integral boundary conditions, we prove existence results of positive solutions depending on real parameters µ 1 and µ 2 . In the scalar case, Bourguiba and Toumi in [3] considered the following semipositone problem…”

Existence results for fractional differential equations in presence of upper and lower solutions

“…We refer the reader to [6,10,24] and the references therein, for some applications. Concerning the study of the existence of solutions for fractional differential equations, in the last few decades, many different analytical techniques and methods have been applied such as iterative methods [21,28], the Mawhin continuation theorem [21], the upper and lower solutions method [15,25], or the use of fixed point theory [5].…”