Numerical methods for solving nonlinear fractional differential equations: convergence and stability analysis

Abstract

This paper presents a comprehensive analysis of numerical methods for solving nonlinear fractional differential equations (FDEs). We examine several numerical techniques including fractional Adams-Bashforth-Moulton methods, predictor-corrector approaches, and spectral methods. The convergence properties and stability characteristics of these methods are rigorously analyzed. Theoretical results are supported by numerical experiments demonstrating the efficiency and accuracy of the methods. The numerical solution of these equations presents unique challenges due to the non-local nature of fractional operators and nonlinearity.