Numerical schemes for modelling time-fractional dynamics of non-isothermal diffusion in soils

AbstractWe present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.

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Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes

Computational Mechanics ◽

10.1007/s00466-021-02051-z ◽

2021 ◽

Author(s):

François Kimmig ◽

Philippe Moireau ◽

Dominique Chapelle

Keyword(s):

Hierarchical Modeling ◽

Force Generation ◽

Numerical Schemes ◽

Cardiac Muscles

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Fractional dynamics of 2019-nCOV in Spain at different transmission rate with an idea of optimal control problem formulation

Alexandria Engineering Journal ◽

10.1016/j.aej.2021.07.005 ◽

2021 ◽

Author(s):

Pushpendra Kumar ◽

Vedat Suat Erturk ◽

Kottakkaran Sooppy Nisar ◽

Wasim Jamshed ◽

Mohamed S. Mohamed

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Transmission Rate ◽

Problem Formulation ◽

Fractional Dynamics

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General Fractional Dynamics

Mathematics ◽

10.3390/math9131464 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1464

Author(s):

Vasily E. Tarasov

Keyword(s):

Fractional Calculus ◽

Exact Solutions ◽

Arbitrary Order ◽

Nonlinear Dynamical Systems ◽

Fractional Integrals ◽

Fractional Dynamics ◽

Fractional Systems ◽

Nonlinear Dynamical ◽

Fractional Differential ◽

Solutions Of Equations

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general form of nonlocality, which can be described by general-form operator kernels and not by its particular implementations and representations. In this paper, the concept of “general nonlocal mappings” is proposed; these are the exact solutions of equations with GFI and GFD at discrete points. In these mappings, the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs. These types of kernels are used in general fractional integrals and derivatives for the initial equations. Using general fractional calculus, we considered fractional systems with general nonlocality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order were also used to derive general nonlocal mappings. The exact solutions for these general fractional differential and integral equations with kicks were obtained. These exact solutions with discrete timepoints were used to derive general nonlocal mappings without approximations. Some examples of nonlocality in time are described.

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