Sania QureshiAmanullah SoomroIoannis K. ArgyrosKrzysztof GdawiecAli AkgülMarwan Alquran2025-02-032025-02-032025-04Qureshi, S., Soomro, A., Argyros, I. K., Gdawiec, K., Akgül, A., & Alquran, M. (2025). Use of fractional calculus to avoid divergence in newton-like solver for solving one-dimensional nonlinear polynomial-based models. Communications in Nonlinear Science and Numerical Simulation, 108631.1007-5704https://doi.org/10.1016/j.cnsns.2025.108631https://hdl.handle.net/20.500.12604/8487There are many different fields of study where nonlinear polynomial-based models arise and need to be solved, making the study of root-finding iterative solvers an important topic of research. Our goal was to use the two most significant fractional differential operators, Caputo and Riemann–Liouville, and an existing time-efficient three-step Newton-like iterative solver to address the growing interest in fractional calculus. The classical solver is preserved alongside a damping term created within it that tends to 1 as the fractional order α approaches 1. The solvers’ local and semi-local convergence are investigated, and the stability trade-off with convergence speed is discussed at length. The suggested fractional-order solvers are tested on a number of nonlinear one-dimensional polynomial-based problems that come up in image processing, mechanical design, and civil engineering, such as beam deflection; and many more.eninfo:eu-repo/semantics/closedAccessBasins of attractionFractional order derivativeLocal and semilocal analysisStabilityjournal-article143Q12-s2.0-8521611468410.1016/j.cnsns.2025.108631