Solution of Time-Fractional Partial Differential Equations via the Natural Generalized Laplace Transform Decomposition Method

This work presents an efficient analytical technique for obtaining approximate solutions to time-fractional system partial differential equations. The proposed method combines the Natural generalized Laplace transform with the decomposition method to construct a systematic solution framework. A general formulation of the method is developed for a broad class of time-fractional system equations. In particular, we check the validity and effectiveness of the approach by providing three illustrative examples, confirming its accuracy and applicability in solving both linear and nonlinear fractional problems.