Knowledge graphs (KGs) have evolved into foundational infrastructures for natural language processing and recommendation systems. The persistent challenges of long-tail relation distributions and structural sparsity in KGs have driven few-shot knowledge graph completion (FKGC) to the forefront of knowledge engineering research. This methodology confronts acute data paucity issues, where conventional neural architectures frequently succumb to overfitting under extreme low-resource conditions, resulting in compromised generalization performance. To address these limitations, a Dynamic Relational Meta-Learning framework with Kolmogorov-Arnold Network integration (KAN-DRML) is proposed which introduces three key innovations: (1) A dynamic relation discriminator that dynamically fuses support set instances with graph context features to enhance relational reasoning; (2) A KAN-based relational meta-learner generating topology-aware embeddings via nonlinear semantic composition; (3) An embedding learner based on bilevel optimization, enabling rapid parameter adaptation via gradient updates. Extensive evaluations on NELL-One and Wiki-One demonstrate KAN-DRML’s superiority in few-shot scenarios compared to baseline models.