A comparative framework for convergence analysis of perturbation series techniques in nonlinear fractional quadratic differential equations.

ABSTRACT: This study tackles the challenge of obtaining highly accurate approximate solutions for nonlinear fractional differential equations, which often lack exact solutions due to their inherent complexity. A unified perturbation framework is proposed based on homotopy topology theory, enabling multiple formulations depending on the number of convergence-control parameters. Through dynamic adjustment of these parameters, the Homotopy Method achieves enhanced precision, particularly for fractional-order models exhibiting long-memory behavior. Numerical results clearly demonstrate that increasing the number of convergence parameters leads to significantly improved accuracy. Supported by detailed graphs and tables, the proposed approach proves to be a flexible, robust, and reliable tool for solving

SUBMITTER: Hashim DJ 

PROVIDER: S-EPMC12747413 | biostudies-literature | 2025

REPOSITORIES: biostudies-literature