Authors : Mansi Shinde; Soni Pathak

Volume/Issue : Volume 11 - 2026, Issue 6 - June

Google Scholar : https://tinyurl.com/47anpk2p

Scribd : https://tinyurl.com/yy3cn6zn

DOI : https://doi.org/10.38124/ijisrt/26jun152

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : The stress–strain response of non-Newtonian fluids is highly nonlinear and shows long-term memory effects, anomalous relaxation behavior, and frequency-dependent responses when stress is applied. Some classical viscoelastic models such as the Maxwell, Kelvin–Voigt, and Burgers models [1, 4], are not well suited to the hereditary behavior of polymers, biological tissues, gels, suspensions, or industrial materials. Fractional calculus is an effective mathematical tool for modeling these types of systems because fractional derivatives inherently exhibit nonlocal and memory-dependent effects [3, 5]. This review addresses viscoelastic models for non-Newtonian fluid dynamics using a fractional approach. The Caputo derivative, Riemann-Liouville derivative Caputo-Fabrizio derivative and Atangana-Baleanu derivative are some known fractional operators. They have been discussed in terms of interpretation, constitutive behavior and rheology [5, 8 13]. When comparing models like Maxwell, Kelvin-Voigt, Zener and generalized models we look at key features. These include creep and relaxation behavior, power-law rheology and computational efficiency [1, 4 5]. Recent advances in equations have been summarized. This includes developments, in Navier-Stokes formulations, multi-term and variable-order operators and advanced numerical methods [6, 7 10]. Existing problems in parameter estimation, computational complexity, numerical stability, and experimental validation are also discussed in this paper. Finally, future research directions on the use of machine learning for parameter identification, hybrid CFD–fractional models, adaptive fractional models, and biomedical modeling of rheological properties are indicated in this paper. This review provides a general understanding of the role of fractional viscoelasticity in complex fluid systems.

Keywords : Fractional Calculus, Non-Newtonian Fluids, Viscoelasticity, Memory Effects, Fractional Constitutive Equations, Power-Law Rheology, Fractional Derivatives.

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