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2022 (2)

2018 (1)

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Book
Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures
Authors: --- --- ---
ISBN: 9811046662 9811046654 Year: 2018 Publisher: Singapore : Springer Singapore : Imprint: Springer,

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Abstract

This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting  applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept are motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.


Book
Evolutionary equations : Picard's theorem for partial differential equations, and applications
Authors: --- ---
ISBN: 3030893979 3030893960 Year: 2022 Publisher: Cham Springer Nature

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This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.


Book
Fractional Calculus - Theory and Applications
Author:
Year: 2022 Publisher: Basel MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications.

Keywords

Research & information: general --- Mathematics & science --- Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm-Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Laplace transform --- Mittag-Leffler function --- Grünwald-Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness

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