Fractional modeling in action: A survey of nonlocal models for subsurface transport, turbulent flows, and anomalous materials

JL Suzuki, M Gulian, M Zayernouri, M D'Elia - Journal of Peridynamics and …, 2023 - Springer
Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

Models of viscoelastic materials: A review on historical development and formulation

MV Shitikova, AI Krusser - … , and Experiments of Multiscale Materials: A …, 2022 - Springer
A classification of different mathematical models of viscoelastic materials is presented. The
review covers the classical models of viscoelasticity with integer order derivatives, as well as …

Cascaded fractional model predictive controller for load frequency control in multiarea hybrid renewable energy system with uncertainties

MM Gulzar, D Sibtain, M Khalid - International Journal of …, 2023 - Wiley Online Library
The rapid utilization of electricity has forced the stability of the power system for continuous
operation. Due to difference in demand and generation, the frequency reference point …

Anomalous nonlinear dynamics behavior of fractional viscoelastic beams

JL Suzuki, E Kharazmi… - Journal of …, 2021 - asmedigitalcollection.asme.org
Fractional models and their parameters are sensitive to intrinsic microstructural changes in
anomalous materials. We investigate how such physics-informed models propagate the …

Multiscale nonlocal elasticity: A distributed order fractional formulation

W Ding, S Patnaik, F Semperlotti - International Journal of Mechanical …, 2022 - Elsevier
This study presents a generalized multiscale nonlocal elasticity theory that leverages
distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal …

Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models

Y Qiao, X Wang, H Xu, H Qi - Applied Mathematics and Mechanics, 2021 - Springer
Fractional calculus has been widely used to study the flow of viscoelastic fluids recently, and
fractional differential equations have attracted a lot of attention. However, the research has …

Statistical mechanics of plasticity: Elucidating anomalous size-effects and emergent fractional nonlocal continuum behavior

P Khandagale, L Liu, P Sharma - Journal of the Mechanics and Physics of …, 2024 - Elsevier
Extensive experiments over the decades unequivocally point to a pronounced scale-
dependency of plastic deformation in metals. This observation is fairly general, and broadly …

The direct meshless local Petrov–Galerkin technique with its error estimate for distributed-order time fractional Cable equation

A Habibirad, E Hesameddini, H Azin… - Engineering Analysis with …, 2023 - Elsevier
Distributed-order fractional calculus is a quickly growing concept of the more general area of
fractional calculus that has significant and extensive usage for designing complex systems …

Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators

N Li, X Wang, H Xu, H Qi - Mathematics and Computers in Simulation, 2024 - Elsevier
The magnetohydrodynamic (MHD) flow has been concerned widely for its widespread
adoption in the field of astrophysics, electronics and many other industries over the years …

Integrated radial basis function technique to simulate the nonlinear system of time fractional distributed-order diffusion equation with graded time-mesh discretization

M Abbaszadeh, ARB Salec, AS Jebur - Engineering Analysis with …, 2023 - Elsevier
The distributed-order fractional calculus (DOFC) is a generalization of the fractional calculus
which its application can be found in viscoelasticity, transport processes and control theory …