A Generalized Local Fractional Laplace Transform via a Unified Derivative Operator

Recently, generalized local fractional derivatives have attracted increasing attention due to their ability to model nonlocal and scale-dependent phenomena while preserving locality. In this paper, we introduce a generalized local fractional Laplace transform constructed through a unified derivative operator. This new transform extends the classical Laplace transform to local fractional orders while retaining its fundamental operational properties. The proposed framework provides a consistent analytical tool for the treatment of differential equations involving generalized local fractional derivatives and establishes a natural bridge between classical and local fractional analysis.