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Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations. (English) Zbl 1244.34009

Summary: We are concerned with the existence and uniqueness of positive solutions for the following singular nonlinear (n-1,1) conjugate-type fractional differential equation with a nonlocal term

D 0+ α x(t)+f(t,x(t))=0,0<t<1,n-1<αn,x (k) (0)=0,0kn-2,x(1)= 0 1 x(s)dA(s),

where α2, D 0+ α is the standard Riemann-Liouville derivative, A is a function of bounded variation and 0 1 u(s)dA(s) denotes the Riemann-Stieltjes integral of u with respect to A, dA can be a signed measure.

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