This paper investigates the solvability of a nonlinear kernel-driven fractional integro-differential equation of order \(\varrho \) involving a p-Laplacian-type operator. By exploiting analytical properties of \(\varrho \) -fractional calculus, an explicit integral representation of the solution is derived, highlighting the interplay between fractional memory and nonlinear diffusion mechanisms. The existence of solutions is established via Krasnoselskii’s fixed point theorem in an appropriate Banach space, while uniqueness is guaranteed through Banach’s contraction principle under suitable conditions. To illustrate the applicability of the theoretical results, an example is presented. The obtained results extend and unify several existing models, providing a flexible analytical tool for the study of fractional systems with kernel-type interactions.
