@article{Hussain2025, 
author = {Kashif Hussain and Ala Amourah and Jamal Salah and Ali Fareed Jameel and Nidal Anakira},
title = {Autonomous block method for uncertainty analysis in first-order real-world models using fuzzy initial value problem},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {9614-9636},
keywords = {fuzzy derivative, first-order, two-step, block method, zero-stability, real-life models},
url = {https://www.sciopen.com/article/10.3934/math.2025443},
doi = {10.3934/math.2025443},
abstract = {This article employs fuzzy derivatives and fuzzy differential equations (FDEs) to handle uncertainty in real-world applications. When exact answers are unavailable, numerical approaches are utilized to derive approximations for FDE. The autonomous two-step block method (TBM) with two higher fuzzy derivatives is used to discover optimum solutions to first-order FDEs with greater absolute accuracy. The technique competency is evaluated by analyzing first-order real-world models with fuzzy initial value problems (FIVPs). Using fuzzy calculus principles, we establish a novel universal fuzzification formulation of the TBM approach with the Taylor series. TBM is a convergent, zero-stable, and absolute stability region approach for solving linear and nonlinear fuzzy models, with a focus on regulating the convergence of approximate solutions. The developed method offers approximations for difficulties encountered in real life and is a transformational and workable method for solving first-order FIVPs.}
}