| Summary: | Abstract In this paper, we discuss the existence of positive solutions of the conformable fractional differential equation Tαx(t)+f(t,x(t))=0 $T_{\alpha }x(t)+f(t,x(t))=0$, t∈[0,1] $t\in [0,1]$, subject to the boundary conditions x(0)=0 $x(0)=0$ and x(1)=λ∫01x(t)dt $x(1)= \lambda \int_{0}^{1}x(t)\,\mathrm{d}t$, where the order α belongs to (1,2] $(1,2]$, Tαx(t) $T_{\alpha }x(t)$ denotes the conformable fractional derivative of a function x(t) $x(t)$ of order α, and f:[0,1]×[0,∞)↦[0,∞) $f:[0,1]\times [0,\infty)\mapsto [0,\infty)$ is continuous. By use of the fixed point theorem in a cone, some criteria for the existence of at least one positive solution are established. The obtained conditions are generally weaker than those derived by using the classical norm-type expansion and compression theorem. A concrete example is given to illustrate the possible application of the obtained results.
|
|---|