Existence of positive solutions for a singular fractional boundary value problem

Abstract

We study the existence of positive solutions for a nonlinear Riemann-Liouville fractional differential equation with a sign-changing nonlinearity, subject to multi-point fractional boundary conditions.

Positive Solutions for Singular Semipositone Fractional Differential Equation Subject to Multipoint Boundary Conditions

“…Very recently, Henderson and Luca [1] obtained the existence result of positive solution for the following singular differential equation with fractional derivative: 0+ ( ) + ( , ( )) = 0, 0 < < 1,…”

“…First, the nonlinear term may take negative infinity and change its sign. Compared with [1], permits singularities on the time and the space variables at the same time. Second, the method exploited in this paper is different from that in [1] in essence.…”

“…Compared with [1], permits singularities on the time and the space variables at the same time. Second, the method exploited in this paper is different from that in [1] in essence. More precisely, height functions with their integrations on some special bounded set are utilized to get the existence result for positive solutions of BVP (1)- (2).…”

Positive solutions of semipositone singular fractional differential systems with a parameter and integral boundary conditions

“…In [29], Henderson, Luca and Tudorache discussed the systems of nonlinear fractional di erential equations with integral boundary conditions…”

Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives

“…Boundary value problems of fractional differential equations have been investigated for many years. Now, there are many papers dealing with the problem for different kinds of boundary value conditions such as multi-point boundary condition (see [5][6][7][8][9][10]), integral boundary condition (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24]), and many other boundary conditions (see [25][26][27][28][29][30][31][32]). …”