Abstract
This work deals with a boundary value problem for a nonlinear multi-point fractional differential equation on the infinite interval. By constructing the proper function spaces and the norm, we overcome the difficulty following from the noncompactness of $[0, \infty)$ . By using the Schauder fixed point theorem, we show the existence of one solution with suitable growth conditions imposed on the nonlinear term.
Highlights
1 Introduction In this paper, we consider the existence of solution of boundary value problem for a nonlinear multi-point fractional differential equation, Dα +u(t) = f t, u(t), Dα +– u(t), t ∈ J := [, +∞), ( . )
The existence and multiplicity of solutions to boundary value problems of fractional differential equations on the infinite interval have been investigated in recent years [ – ]
Agarwal et al [ ] established existence results of solutions for a class of boundary value problems involving the Riemann-Liouville fractional derivative on the half line by using the nonlinear alternative of Leray-Schauder type combined with the diagonalization process
Summary
1 Introduction In this paper, we consider the existence of solution of boundary value problem for a nonlinear multi-point fractional differential equation, Dα +u(t) = f t, u(t), Dα +– u(t) , t ∈ J := [ , +∞), In [ ], the authors considered the three-point boundary value problem of a coupled system of the nonlinear fractional differential equation By using the Schauder fixed point theorem, they obtained at least one solution of this problem.
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