Nonlocal-in-time kinetic energy in nonconservative fractional systems, disordered dynamics, jerk and snap and oscillatory motions in the rotating fluid tube

El-Nabulsi, Rami Ahmad

doi:10.1016/j.ijnonlinmec.2017.04.010

Cited by 45 publications

(5 citation statements)

References 32 publications

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“…Time-nonlocal models have been receiving an increasing interest in the physics and engineering communities [113][114][115] which also generated renewed attention to nonconservative and dissipative systems already mentioned in Section 2.1. Some of the developed approaches, such as the nonlocal-in-time kinetic energy proposal [116], in addition to its numerous applications [117][118][119], may also be usefuful in shedding further light into the relationship between classical and quantum mechanics.…”

Section: Nonlocality In Timementioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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Section: Nonlocality In Timementioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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“…Note that: DβDβ=(false0T0τfalse¯)β−1(D2+1−βτ¯D):=(false0T0τfalse¯)β−1false(B1−βfalse)τfalse¯,where false(B1−βfalse)τfalse¯:=D2+1−βτ¯D is the Bessel operator [85]. Several applications of HFTDO were discussed in [86–93]. However, for very large time, we can use the following asymptotic rule false(B1−βfalse)τfalse¯≈D2.…”

Section: Introductionmentioning

confidence: 99%

“…is the Bessel operator [85]. Several applications of HFTDO were discussed in [86][87][88][89][90][91][92][93]. However, for very large time, we can use the following asymptotic rule ðB 1Àb Þ t % D 2 .…”

Section: Introductionmentioning

confidence: 99%

Emergence of lump-like solitonic waves in Heimburg–Jackson biomembranes and nerves fractal model

El-Nabulsi

2022

J. R. Soc. Interface.

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The aim of this study is to extend the soliton propagation model in biomembranes and nerves constructed by Heimburg and Jackson for the case of fractal dimensions. Our analyses are based on the product-like fractal measure concept introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media and electromagnetic fields. The mathematical model presented in the paper is formulated for only a part of a single nerve cell (an axon). The analytical and numerical envelop soliton of this equation are reported. The results obtained prove the emergence of lump-type solitonic waves in nerves and biomembranes. In particular, these waves decay algebraically to the background wave in space direction. This scenario is viewed as a particular class of rational localized waves which are solutions of the integrable Ishimori I equation and the (2 + 1) Kadomtsev–Petviashvili I equation. The effects of fractal dimensions are discussed and were found to be significant to some extents.

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“…This involves a third derivative of x and has been found to have numerous applications in many areas of science, such as electrical circuits, laser physics, mechanics, acoustics, and dynamical processes. We refer the reader to [2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

Han

Zhang

2021

Axioms

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By coincidence degree theory due to Mawhin, some sufficient conditions for the existence of solution for a class of coupled jerk equations with multi-point conditions are established. The new existence results have not yet been reported before. Novel coupled fractional jerk equations with resonant boundary value conditions are discussed in detail for the first time. Our work is interesting and complements known results.

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Nonlocal-in-time kinetic energy in nonconservative fractional systems, disordered dynamics, jerk and snap and oscillatory motions in the rotating fluid tube

Cited by 45 publications

References 32 publications

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Emergence of lump-like solitonic waves in Heimburg–Jackson biomembranes and nerves fractal model

On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

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