Abstract: The author considered the solvability of a class of Riemann-Liouville fractional boundary value resonance problems with infinite multipoint boundary conditions. Firstly, by using the fixed point theorem of cone extension and compression, the author obtained the existence of a positive solution when the nonlinear term f satisfied a certain condition. Secondly, under the condition that the nonlinear term f satisfied stronger conditions, the results of three positive solutions of the problem were obtained by using Leggett-Williams fixed point theorem.

Key words: fractional differential equation, infinite multipoint boundary value problem, resonance, fixed point theorem, positive solution