This research examines generalized boundary value problems of the -Hilfer fractional differential equations of order 2 < α < 3 and n − 1 < α < n (n ≥ 4), type β ∈ [0, 1] under two different initial conditions. Through equivalent fractional integral equations, the existence and uniqueness of a solution have been demonstrated. This study relies on a variety of fractional calculus tools aswell as nonlinear theorems due to Leray–Schauder and Schaefer. To conclude, examples are provided to illustrate how the key results might be justified.
