主题词：Fractional Differential Equations Solutions; Mathematical Dynamics and Fractals; Complex Systems and Time Series Analysis; Theoretical and Computational Physics; Chaos control and synchronization; Nonlinear Waves and Solitons; Advanced Mathematical Theories and Applications; Nonlinear Differential Equations Analysis; Fractal and DNA sequence analysis; Neural Networks and Applications; Complex Network Analysis Techniques; Mathematical and Theoretical Epidemiology and Ecology Models; Iterative Methods for Nonlinear Equations; Hydraulic Fracturing and Reservoir Analysis; Differential Equations and Numerical Methods; Mathematical Inequalities and Applications; Hydrocarbon exploration and reservoir analysis; Cellular Automata and Applications; Topological and Geometric Data Analysis; Statistical Mechanics and Entropy; Nonlinear Photonic Systems; Stochastic processes and statistical mechanics; Groundwater flow and contamination studies; Advanced Control Systems Design; Financial Risk and Volatility Modeling