Abstract:
We consider an interior boundary-value problem for a linear, ordinary differential equation with an operator of fractional, discretely distributed differentiation. The boundary conditions connect the values of the unknown solution at the ends of the interval with the values at interior points. Green's function is constructed and the theorem of the existence and uniqueness of a solution is proved.
Keywords:interior boundary value problem, Green's function, Caputo derivative, fractional ordinary differential equation, operator of discretely distributed differentiation.