Fractional modeling in action: A survey of nonlocal models for subsurface transport, turbulent flows, and anomalous materials
Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …
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 …
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
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 …
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 …
anomalous materials. We investigate how such physics-informed models propagate the …
Multiscale nonlocal elasticity: A distributed order fractional formulation
This study presents a generalized multiscale nonlocal elasticity theory that leverages
distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal …
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 …
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 …
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 …
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 …
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 …
which its application can be found in viscoelasticity, transport processes and control theory …