Linguistic Sustainability: An Innovative Technique for Simulating Constant and Variable Fractional‐Order Dynamics

ABSTRACT There are dozens of languages spoken worldwide, but due to linguistic shifts and rivalry, many of them are in danger of becoming extinct. A vital component, therefore, is linguistic sustainability because cultural sustainability depends on language preservation. To represent linguistic sustainability, which traditional models do not adequately present, this work presents a novel fractional‐order method that uses both constant and variable fractional‐order derivatives. The significance of the arbitrary order derivative and the theoretical conclusions we got were validated by implementing a recently suggested Toufik–Atangana numerical technique with Caputo (C), Caputo–Fabrizio (CF), and Atangana Balaneau Caputo (ABC) fractional derivatives. Additionally, a comparison between the Mathematica NDSolve approach and the integer order Toufik‐Atangana method was done. This innovative method provides insightful information for language preservation plans, allowing linguists and policymakers to create more potent interventions to save endangered languages.