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In the current paper, we intend to check the existence aspects of solutions for a category of the multi‐point boundary value problem (BVP) involving a p$$ p $$‐Laplacian differential operator within the generalized fractional derivatives depending on another function. Based on two fixed point results attributed to Schaefer and Banach, the desired results are verified. Further, the continuity of solutions in terms of inputs (fractional orders, associated parameters, and appropriate function) is extensively discussed. A simulative example is prepared to demonstrate the applications of the obtained results. [ABSTRACT FROM AUTHOR]