scholarly journals On the fractional deformation of a linearly elastic bar

2020 ◽  
Vol 29 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Konstantinos A. Lazopoulos ◽  
Anastasios K. Lazopoulos
Keyword(s):  
Fractional Derivatives ◽  
Axial Stress ◽  
Differential Topology ◽  
Local Character ◽  
Initial Space ◽  
Mathematical Properties ◽  
Elastic Bar ◽  
Fractional Analysis ◽  
Non Local ◽  
New Space

AbstractFractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented.

scholarly journals Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Optimality Conditions ◽  
Fractional Derivatives ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Derivative Operator ◽  
Sir Epidemic ◽  
Non Local

<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory effects. Existence and uniqueness of solution for the proposed fractional model is proved. Existence of an optimal control is also established. Then, necessary optimality conditions are derived. As a consequence, a characterization of the optimal control is given. Lastly, numerical results are given with the aim to show the effectiveness of the proposed control strategy, which provides significant results using the AB fractional derivative operator in the Caputo sense, comparing it with the classical integer one. The results show the importance of choosing very well the fractional characterization of the order of the operators.</p>

Developing Institutions for the New Space Race

2019 ◽  
pp. 99-115
Author(s):  
Luis Alfonso Dau ◽  
Elizabeth M. Moore ◽  
James Arie Figgins ◽  
Julián Martínez-Rincón
Keyword(s):  
State Level ◽  
Strategic Choices ◽  
World Systems Theory ◽  
Descriptive Case Study ◽  
Global Consensus ◽  
Initial Space ◽  
Nation States ◽  
Space Race ◽  
New Space

This chapter examines the dynamic of the major actors in today's new space race. The initial space race featured nation-states as the primary actors. However, the current space race has undergone privatization and now features corporations as additional key players, along with developing nations. The result is the semi-private commoditization of a public good that crosses through different hemispheres, as well as competition between actors from both the firm and state level. Building on world systems theory and institutional theory, this chapter argues that the privatization of space exploration mandates the construction of inter-hemispheric institutional frameworks that apply globally. A descriptive case study that juxtaposes India and SpaceX offers foundational insight into how inter-hemispheric institutions are created. Given the challenging parity between state sovereignty and global consensus and its influence on firm behavior, this chapter proposes an exploratory examination of the processes and strategic choices behind inter-hemispherization to incite future scholarship.

On a new modified fractional analysis of Nagumo equation

2019 ◽  
Vol 12 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Khaled M. Saad ◽  
Si̇nan Deni̇z ◽  
Dumi̇tru Baleanu
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Fractional Derivatives ◽  
Transform Method ◽  
Average Residual ◽  
Homotopy Analysis ◽  
Fractional Analysis ◽  
Nagumo Equation ◽  
Modified Equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

scholarly journals Turbulence through the Spyglass of Bilocal Kinetics

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 539 ◽  
Author(s):  
Gregor Chliamovitch ◽  
Yann Thorimbert
Keyword(s):  
Turbulent Flows ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Pressure Tensor ◽  
Kinetic Description ◽  
Balance Equations ◽  
Coupling Term ◽  
Navier Stokes Equation ◽  
Local Character ◽  
Non Local

In two recent papers we introduced a generalization of Boltzmann’s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann’s kinetic equation. The present paper aims to investigate how the essentially non-local character of turbulent flows can be addressed through this bilocal kinetic description, instead of the more standard approach through the local Euler/Navier–Stokes equation. Balance equations appropriate to this kinetic scheme are derived and closed so as to provide bilocal hydrodynamical equations at the non-viscous order. These equations essentially consist of two copies of the usual local equations, but coupled through a bilocal pressure tensor. Interestingly, our formalism automatically produces a closed transport equation for this coupling term.

scholarly journals Multiscalar moral economy

Focaal ◽  
2020 ◽  
pp. 1-14
Author(s):  
Tijo Salverda
Keyword(s):  
Moral Economy ◽  
Land Grabbing ◽  
Rural Residents ◽  
Local Character ◽  
Economic Exchanges ◽  
Local Actors ◽  
Non Local ◽  
Heuristic Device ◽  
Moral Economic

This article addresses the relevance of the moral economy concept in light of unequal socioeconomic relations between a European agribusiness and rural residents in Zambia. It argues that the moral economy concept offers a helpful heuristic device for analyzing how relationships are constituted, negotiated, and contested among interdependent actors with “opposing” socioeconomic interests. To explain the dynamics of their relationships, however, the moral economy concept has to extend beyond its usual, spatially restricted (i.e., local) focus. Instead, “external,” distant, non-local actors, such as foreign critics concerned about “land grabbing,” also influence the local character of moral-economic exchanges between the agribusiness and rural residents. Hence, the article proposes a multiscalar perspective to account for the influence of a wider array of actors.

scholarly journals Non-local fractional derivatives. Discrete and continuous

2017 ◽  
Vol 449 (1) ◽  
pp. 734-755 ◽  
Author(s):  
Luciano Abadias ◽  
Marta De León-Contreras ◽  
José L. Torrea
Keyword(s):  
Fractional Derivatives ◽  
Non Local

ANALYTIC CONTINUATION OF OPERATORS APPLICATIONS: FROM NUMBER THEORY AND GROUP THEORY TO QUANTUM FIELD AND STRING THEORIES

1999 ◽  
Vol 11 (04) ◽  
pp. 463-501 ◽  
Author(s):  
S. C. WOON
Keyword(s):  
Number Theory ◽  
Analytic Continuation ◽  
Particle Physics ◽  
Fractional Derivatives ◽  
Bernoulli Polynomials ◽  
Local Effect ◽  
Quantum Field ◽  
Matrix Representations ◽  
Complex Power ◽  
Non Local

We are used to thinking of an operator acting once, twice, and so on. However, an operator can be analytically continued to the operator raised to a complex power. Applications include (s,r) diagrams and an extension of Fractional Calculus where commutativity of fractional derivatives is preserved, generating integrals and non-standard derivations of theorems in Number Theory, non-integer power series and breaking of Leibniz and Chain rules, pseudo-groups and symmetry deforming models in particle physics and cosmology, non-local effect in analytically continued matrix representations and its connection with noncommutative geometry, particle-physics-like scatterings of zeros of analytically continued Bernoulli polynomials, and analytic continuation of operators in QM, QFT and Strings.

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