Throughout this work, the analysis is carried out in uniformly smooth and reflexive Banach spaces endowed with a weakly continuous duality mapping. This work presents a novel modified four-step Halpern-type iterative sequence for the generalized (α,β,γ,δ)-nonspearding mappings and examining its behavior of convergence to a fixed point. This modification is obtained by integrating the μ-Krasnosel’skii operator into the structure of the original four-step iterative scheme. A strong convergence result is established for the resulting RS-iteration under the stated assumptions. The convergence performance is examined through a numerical experiment, and the corresponding outcomes are displayed in numerical and graphical forms. To demonstrate the practical relevance of the theoretical findings, the developed iterative framework is applied to an SEIR epidemic system described by a Caputo fractional differential model. These results extend the available convergence theory for fixed-point algorithms and illustrate its potential usefulness in mathematical modelling.