Forecasting time series data especially in volatile sectors like financial markets, shows significant challenges due to non-linearity, non-stationarity and noise in the data. Traditional forecasting models most likely fail to generalize effectively across varying tasks without extensive retraining. This study investigates the application of meta learning techniques, particularly First-Order Model-Agnostic Meta-Learning (FOMAML) and Reptile, to make adaptability and generalization better in time series forecasting tasks. An extensive empirical study was done using three neural networks as base models, namely Long Short Term Memory (LSTM), Gated Recurrent Unit (GRU) and Feed Forward Neural Network (FFNN) applied to four real-world stocks: TCS, TATASTEEL, GRASIM and DJIAHD. The models were evaluated under few-shot learning(defined here as 211-shot learning using sliding window samples) conditions with varying iteration counts(outer loops or epochs) and their effectiveness was checked using some common standard metrics like RMSE(Root Mean Squared Error), MAE(Mean Absolute Error) and R²(Coefficient of Determination). Outcomes have shown that meta-learning approach notably performs much better than traditional models with MAML(First Order) in particular showing quicker task adaptation as well as stable convergence behavior, especially when it used with GRU and LSTM as base models, as validated empirically on the GRASIM dataset where the MAML with LSTM configuration attained around 81.9\% reduction in RMSE (dropping the value from 622.94 to 112.60 over the iterations). In all four stocks, reptile shows relatively steady performance. The study validates the potential of meta-learning as a powerful framework for time series forecasting problem in dynamic settings which offers robust algorithmic foundation for numerous future financial modeling applications.