A robust wavelet-based numerical algorithm with error analysis for fractional Emden–Fowler BVPs under nonlocal boundary effects

Abstract

This work presents an efficient and unified numerical framework for solving fractional-order Emden–Fowler differential equations subject to diverse boundary conditions, including initial conditions, Dirichlet–Robin, Neumann–Robin, and three-point nonlocal boundary conditions. The proposed approach is based on Taylor wavelets, their Riemann–Liouville (RL) integral, and a uniform collocation point strategy. By employing Taylor wavelets and their RL integrals, the underlying singular fractional problem is systematically transformed into a system of nonlinear algebraic equations. At the same time, the uniform collocation scheme ensures computational simplicity and stability. The resulting algebraic system can be efficiently solved using Newton–Raphson’s method, yielding highly accurate approximate solutions. The method effectively handles the intrinsic singularity at the origin directly and accommodates both local and nonlocal boundary conditions within a single computational framework. Numerical experiments demonstrate the accuracy, convergence behavior, and computational efficiency of the proposed technique, highlighting its potential as a reliable tool for analyzing fractional Emden–Fowler models arising in various scientific and engineering applications.