Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

Abstract

We establish the existence and uniqueness of a positive solutionufor the following fractional boundary value problem:Dαu(x)=−a(x)uσ(x),x∈(0,1)with the conditionslimx→0+⁡x2−αu(x)=0,u(1)=0, where1<α≤2,σ∈(−1,1), andais a nonnegative continuous function on(0,1)that may be singular atx=0orx=1. We also give the global behavior of such a solution.

Existence and Global Asymptotic Behavior of Positive Solutions for Superlinear Singular Fractional Boundary Value Problems

“…For further related results, we refer the reader to [12][13][14][15][16][17][18][19][20][21] and the references therein. Motivated by the approach used in [11], we consider the problem:…”

Existence of a positive solution for a singular fractional boundary value problem with fractional boundary conditions using convolution and lower order proble

“…The study of singular fractional boundary value problems has been extensive and growing in recent years. Several authors have used a range of fixed point theorems to establish the existence of positive solutions for various types of problems [1,10,12,[16][17][18][19]. As a specific recent example, we point the reader to Henderson and Luca [7] for their study of the singular fractional problem…”

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

“…It is worth mentioning that many authors studied fractional differential equations which were applied in many fields such as physics, mechanics, chemistry, and engineering; (see, for instance [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and the references therein).…”