A COMPUTATIONAL INTELLIGENCE APPROACH FOR SOLVING MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATIONS IN ENGINEERING SYSTEMS.
Keywords:
Fractional Differential Equations (FDEs), Caputo Derivative, Collocation Method, Polynomial Approximation, Numerical Analysis, Viscoelastic Systems, Windkessel Model, Memory Effect, Engineering Applications, Computational FrameworkAbstract
This study presents a computational intelligence-based framework for solving multi-term fractional differential equations (MT-FDEs) common in engineering systems. The approach combines polynomial series expansion with a collocation technique to convert complex fractional models into solvable algebraic systems. Using Caputo-type derivatives, the method effectively captures memory and hereditary effects in materials and systems. Two engineering applications a viscoelastic bridge deck and a fractional Windkessel blood flow model demonstrate the accuracy and stability of the approach. The numerical results show excellent agreement with exact analytical solutions, producing negligible errors. The findings confirm the method’s efficiency and reliability in modeling real-world systems that exhibit fractional-order behavior, with potential for wider application in nonlinear and multidimensional engineering problems.
