Accurate prediction of time-to-event outcomes is critical for clinical decision-making, treatment planning, and resource allocation in modern healthcare. While classical survival models such as Cox remain widely adopted in standard practice, they rely on restrictive assumptions, including linear covariate relationships and proportional hazards over time, that often fail to capture real-world clinical dynamics. Recent deep learning approaches like DeepSurv and DeepHit offer improved expressivity but sacrifice interpretability, limiting clinical adoption where trust and transparency are paramount. Hybrid models incorporating Kolmogorov-Arnold Networks (KANs), such as CoxKAN, have begun to address this trade-off but remain constrained by the semi-parametric Cox framework. In this work we introduce SurvKAN, a fully parametric, time-continuous survival model based on KAN architectures that eliminates the proportional hazards constraint. SurvKAN treats time as an explicit input to a KAN that directly predicts the log-hazard function, enabling end-to-end training on the full survival likelihood. Our architecture preserves interpretability through learnable univariate functions that indicate how individual features influence risk over time. Extensive experiments on standard survival benchmarks demonstrate that SurvKAN achieves competitive or superior performance compared to classical and state-of-the-art baselines across concordance and calibration metrics. Additionally, interpretability analyses reveal clinically meaningful patterns that align with medical domain knowledge.