A Collocation-Based Framework for the Computational Solution of Mixed-Order Fractional Differential Equations

The present research introduces a structured computational modality utilizing collocation techniques regarding solving mixed-order fractional differential equations under Caputo's interpretation of initial conditions. The governing problem is transformed into an equivalent integral formulation, subsequently leading to a system of structured linear equations. These equations are efficiently addressed through optimized matrix inversion methods, with the computed values integrated into the computed approximation framework. The reliability and efficiency of the suggested methodology can be considered validated through computational case studies, showcasing its robustness in achieving reliable numerical solutions.