关键词: φ-Hilfer分数阶导数, Mawhin的重合度理论, Fredholm算子, 边值问题, 共振

Abstract: By using Mawhin’s coincidence degree theory, we  study the existence of  solutions for the φ-Hilfer fractional order Riemman-Stieltjes integral boundary value problem. The results show that the solutions of φ-Hilfer fractional differential equation exist under the Riemann-Stieltjes integral boundary value conditions in suitable Banach spaces.

Key words: φ-Hilfer fractional derivative, Mawhin’s coincidence degree theory, Fredholm operator, boundary value problem, resonance