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Existence results for boundary value problems with non-linear fractional differential equations. (English) Zbl 1198.26008

The authors study the boundary value problem for the nonlinear fractional differential equation

c D α y(t)=f(t,y),t[0,T]

with integral boundary conditions

y(T)-y ' (T)= 0 T g(s,y)ds,y(T)+y ' (T)= 0 T h(s,y)ds,

where 1<α2 and c D α y(t) is the Caputo fractional derivative, problems of such a kind arise in applications.

Under various assumptions on f(t,y), g(t,y) and h(t,y) they prove four theorems on the existence of the solution of the problem. In one of them, the uniqueness is also proved.

26A33Fractional derivatives and integrals (real functions)