Abstract
We are concerned with a type of fractional differential equations attached to boundary conditions. We investigate the existence of positive solutions and negative solutions via global bifurcation techniques.
Highlights
Boundary value problems of nonlinear fractional differential equations have been studied extensively in recent years
Little of the previous research is involved with both global bifurcation techniques and fractional differential equations
We will deal with fractional differential equations via global bifurcation techniques
Summary
Boundary value problems of nonlinear fractional differential equations have been studied extensively in recent years (see, for instance, [ – ] and the references therein). Inspired by [ ], we will tackle the following fractional differential equation attached to boundary conditions: Dα +u(t) + rf (t, u(t)) = , t ∈ ( , ), tn–αu(n– )(t)|t= = tn–αu(n– )(t)|t= = · · · = tn–αu(t)|t= = u( ) = ,. (C+ ) There exists a nonnegative function a+∞ ∈ C[ , ] such that tn– ( – t)n– f (t, x) lim x→+∞. The Riemann-Liouville fractional derivative of order α > of a continuous function g : ( , +∞) → R is defined by.
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