主题词：Fractional Differential Equations Solutions; Nonlinear Differential Equations Analysis; Differential Equations and Numerical Methods; Differential Equations and Boundary Problems; Nonlinear Partial Differential Equations; Iterative Methods for Nonlinear Equations; Advanced Control Systems Design; Advanced Mathematical Modeling in Engineering; Stability and Controllability of Differential Equations; Numerical methods in inverse problems; Mathematical functions and polynomials; Numerical methods in engineering; Numerical methods for differential equations; Advanced Harmonic Analysis Research; Stochastic processes and financial applications; Advanced Mathematical Physics Problems; Diverse Scientific and Economic Studies; Thermoelastic and Magnetoelastic Phenomena; Mathematical Analysis and Transform Methods; Diverse Perspectives in Modern Studies; Nonlinear Waves and Solitons; Mathematical and Theoretical Analysis; Statistical Mechanics and Entropy; Mathematical and Theoretical Epidemiology and Ecology Models; Mathematical Dynamics and Fractals