An efficient computational technique for differential systems under epistemic uncertainty

Abstract

. This paper presents an innovative framework for addressing the solutions of non-homogeneous lin
ear systems of differential equations by employing neutrosophic forcing functions and neutrosophic numbers as
 initial conditions. In our study, the forcing function is treated as a neutrosophic set of real-valued functions,
 which is assumed to be hexagonal. This technique differs from existing approaches by representing the solution
 as a neutrosophic set of real vector functions (a neutrosophic bunch), rather than as a vector of neutrosophic
 functions. Each component of this solution set satisfies the system to varying degrees of truth, indeterminacy,
 and falsity, capturing the multi-dimensional uncertainty inherent in complex systems. The solution will be in the
 form of a neutrosophic set, with (α,β,γ)-cuts representing parallelepipeds that describe the uncertainty bound
aries. An important contribution of this study is the comparative analysis with the differential inclusion-based
 method. Unlike differential inclusions, which often overestimate uncertainties and can lose essential qualita
tive properties such as periodicity and boundedness, the proposed approach preserves these characteristics and
 produces narrower, more precise solution sets. The method avoids the divergence of uncertainty over time by
 fixing admissible functions across the entire interval. This comparative insight shows the effectiveness of the
 proposed approach in maintaining structural integrity in dynamic systems with inconsistent or incomplete data.
 A numerical example illustrates its practicality and robustness

DOI: 10.5281/zenodo.16934569