A novel numerical method for solving fractional delay integro-differential algebraic equations

Abstract

This paper introduces a new treatment of Least Squares Support Vector Machines (LS-SVMs) method for solving fractional order delay integro-differential algebraic equations (FDIDAEs). LS-SVMs are utilized to approximate solutions by transforming the FDIDAEs into a constrained optimization problem. The solutions are represented by weighted shifted Legendre polynomials with biases over the problem’s domain. The solution procedure involves systematically determining the unknown weights and biases. Illustrative examples are provided to demonstrate the effectiveness of the proposed methodology. The study also presents a comparison with solutions obtained via fractional Physics-Informed Neural Networks Method.