Green energy is very important for developing new cities with high energy consumption, in addition to helping environment preservation. Integrating solar energy into a grid is very challenging and requires precise forecasting of energy production. Recent advances in Artificial Intelligence have been very promising. Particularly, Deep Learning technologies have achieved great results in short-term time-series forecasting. Thus, it is very suitable to use these techniques for solar energy production forecasting. In this work, a combination of a Convolutional Neural Network (CNN), a Long Short-Term Memory (LSTM) network, and a Transformer was used for solar energy production forecasting. Besides, a clustering technique was applied for the correlation analysis of the input data. Relevant features in the historical data were selected using a self-organizing map. The hybrid CNN-LSTM-Transformer model was used for forecasting. The Fingrid open dataset was used for training and evaluating the proposed model. The experimental results demonstrated the efficiency of the proposed model in solar energy production forecasting. Compared to existing models and other combinations, such as LSTM-CNN, the proposed CNN-LSTM-Transformer model achieved the highest accuracy. The achieved results show that the proposed model can be used as a trusted forecasting technique that facilitates the integration of solar energy into grids.

The current research focusses on the establishment of an analytical approach known as the Riccati Modified Extended Simple equation Method (RMESEM) for the development and assessment of optical soliton solutions in two important Kairat equations. These models are known as Kairat-X equation (K-XE) and the Kairat-II equation (K-IIE), which describe the trajectory of optical pulses in optical fibres. Using RMESEM, the soliton solutions in five families–the periodic, rational, hyperbolic, rational-hyperbolic, and exponential functional families–are achieved for the targeted models. A set of 3D, 2D, and contour visualisations are presented to visually illustrate the dynamics of some produced optical soliton solutions which demonstrates that the due to the axial-periodic perturbation, the optical soliton solutions exhibit fractal phenomena in the realm of K-IIE whereas in the setting of K-XE the optical solitons adopt the form of kink solitons such as solitary kink, lump-type kink, dromion and periodic kink soliton structures. Moreover, our suggested RMESEM illustrates its usefulness by building a multitude of optical soliton solutions, providing valuable insights into the dynamics of the targeted models and indicating potential uses in addressing other nonlinear models.

This manuscript investigates the existence, uniqueness, and different forms of Ulam stability for a system of three coupled differential equations involving the Riemann–Liouville (RL) fractional operator. The Leray–Schauder alternative is employed to confirm the existence of solutions, while the Banach contraction principle is used to establish their uniqueness. Stability conditions are derived utilizing classical nonlinear functional analysis techniques. Theoretical findings are illustrated with an example. The proposed system generalizes third-order ordinary differential equations (ODEs) with different boundary conditions (BCs).