Abstract
The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + Ī± u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ā² ( 0 ) = 0 , where 2 < Ī± ā¤ 3 and D 0 + Ī± is the Riemann-Liouville fractional derivative.Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated.We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear).2010 Mathematics Subject Classification: 34B15
Highlights
Differential equations of fractional order occur more frequently on different research areas and engineering such as physics, chemistry, economics, etc
Some basic theory for the initial value problems of fractional differential equations involving the Riemann-Lioville differential operator has been discussed by Lakshmikantham et al [11,12], Bai et al [13,14,15,16], Zhang [17], etc
DĪ±0+ u(t) + a(t)f (t, u(t)) = 0, 0 < t < 1, 1 < Ī± ā¤ 2 u(0) = u(1) = 0, and they proved the existence of positive solutions by means of the Krasnoselāskii fixed-point theorem and Legget-Williams fixed-point theorem
Summary
Differential equations of fractional order occur more frequently on different research areas and engineering such as physics, chemistry, economics, etc. In [15], the authors studied the following two-point boundary value problem of fractional order In the paper [18] to appear in this special issue, the authors studied the existence of positive solutions for the following autonomous boundary value problem of fractional order
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