SOLVABILITY OF HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE IN $ \mathbb{R}^M $

In this paper, the solvability of a class of nonlinear Hilfer fractional differential equations boundary value problems is considered at resonance in $ \mathbb{R}^m $. The interesting point is that Hilfer is a more general differential operator that contains both the Riemann-Liouville and the Caputo derivative, and the dimension of the kernel of the fractional differential operator with Rimman-stieltjes integral boundary condition can take any value in $ \{1, 2, \cdots, m\} $. By applying Mawhin's coincidence degree theory, the existence result of solutions is obtained.