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Unbounded solutions for a fractional boundary value problems on the infinite interval. (English) Zbl 1193.34008

Summary: We consider the fractional boundary value problem

D 0+ a u(t)+f(t,u(t))=0,t(0,),α(1,2),u(0)=0,lim t D 0+ a-1 u(t)=βu(ξ),

where D is the standard Riemann-Liouville fractional derivative. By means of fixed point theorems, sufficient conditions are obtained that guarantee the existence of solutions to the above boundary value problem.

MSC:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B40Boundary value problems for ODE on infinite intervals
47N20Applications of operator theory to differential and integral equations
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