Banach空间中分数阶微分方程Robin边值问题解的存在性

Existence of solutions for Robin boundary value problems of fractional differential equation in Banach spaces

讨论了Banach空间E中分数阶微分方程边值问题:-D_(0+)^(β)u(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=θ解的存在性,其中1<β≤2,D_(0+)^(β)是标准的Riemann-Liouville分数阶导数,f:[0,1]×E→E连续.通过非紧性测度的估计技巧,在非线性项f满足较弱增长条件下利用凝聚映射的不动点定理获得了该边值问题解的存在性结果.

The existence of solutions for the boundary value problem of a class of the fractional differential equation-D_(0+)^(β)u(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=θin Banach spaces E is discussed,where 1<β≤2,D_(0+)^(β) is the standard Riemann-Liouville fractional derivative,f:[0,1]×E→E is continuous.The existence of the solution of the boundary value problem is obtained by using the fixed point theorem of condensed mapping under the condition of weak growth of nonlinear terms,by using the estimation technique of noncompactness measure.