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Neural transmission. --- Synapses. --- Synaptic Transmission. --- Nerve transmission --- Nervous transmission --- Neurotransmission --- Synaptic transmission --- Transmission of nerve impulses --- Neural circuitry --- Neurophysiology --- Neurotransmitters --- Transmission, Neural --- Transmission, Synaptic --- Neural Transmission --- Neural Conduction --- Synapses --- Synapse --- Synaptic Transmission --- Nerve endings --- Nerves --- Neural transmission --- Synaptosomes
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.
complexity --- cuckoo search --- magnetic resonance imaging --- fractional calculus --- musical signal --- pinning synchronization --- Fourier transform --- optimal randomness --- fractional-order system --- Mittag-Leffler function --- meaning --- parameter --- diffusion-wave equation --- anomalous diffusion --- Laplace transform --- time-varying delays --- mass absorption --- swarm-based search --- fractional --- adaptive control --- time series --- Hurst exponent --- fractional derivative --- control --- PID --- global optimization --- reaction–diffusion terms --- audio signal processing --- Caputo derivative --- harmonic impact --- fractional complex networks --- heavy-tailed distribution --- impulses --- long memory --- linear prediction
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Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.
fractional wave equation --- dependence on a parameter --- conformable double Laplace decomposition method --- Riemann—Liouville Fractional Integration --- Lyapunov functions --- Power-mean Inequality --- modified functional methods --- oscillation --- fractional-order neural networks --- initial boundary value problem --- fractional p-Laplacian --- model order reduction --- ?-fractional derivative --- Convex Functions --- existence and uniqueness --- conformable partial fractional derivative --- nonlinear differential system --- conformable Laplace transform --- Mittag–Leffler synchronization --- delays --- controllability and observability Gramians --- impulses --- conformable fractional derivative --- Moser iteration method --- fractional q-difference equation --- energy inequality --- b-vex functions --- Navier-Stokes equation --- fractional-order system --- Kirchhoff-type equations --- Razumikhin method --- Laplace Adomian Decomposition Method (LADM) --- fountain theorem --- Hermite–Hadamard’s Inequality --- distributed delays --- Caputo Operator --- fractional thermostat model --- sub-b-s-convex functions --- fixed point theorem on mixed monotone operators --- singular one dimensional coupled Burgers’ equation --- generalized convexity --- delay differential system --- positive solutions --- positive solution --- fixed point index --- Jenson Integral Inequality --- integral conditions
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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.
heteroclinic solutions --- non-instantaneous impulses --- Schauder’s fixed point theory --- dichotomy --- second-order differential/difference/q-difference equation of hypergeometric type --- differential equations --- a priori estimates --- global solutions --- generalized Liouville equation --- Hilbert space --- dissipation --- collocation method --- exponential dichotomy --- Sumudu decomposition method --- three-step Taylor method --- dynamical system --- lower and upper solutions --- problems in the real line --- Nagumo condition on the real line --- SIRS epidemic model --- first order periodic systems --- regular solutions --- Clairin’s method --- coupled nonlinear systems --- Navier–Stokes equations --- Bäcklund transformation --- asymptotic stability --- Caputo fractional derivative --- exponential stability --- difference equations --- lipschitz stability --- strong nonlinearities --- polynomial solution --- integro-differentials --- kinetic energy --- Legendre wavelets --- weak solutions --- discrete Lyapunov equation --- population dynamics --- non-uniform lattices --- Korteweg-de Vries equation --- time-dependent partial differential equations --- mean curvature operator --- functional boundary conditions --- mathematical modelling --- fixed point theory --- limit-periodic solutions --- Arzèla Ascoli theorem --- Miura transformation --- state dependent delays --- ?-Laplacian operator --- divided-difference equations --- effective existence criteria
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Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included.
arithmetic progressions --- weighted quadratic variation --- fractional differential-difference equations --- small deviations --- periodic intensity functions --- realized volatility --- rate of convergence --- host-parasite interaction --- first Chebyshev function --- regularly varying functions --- Cohen and Grossberg neural networks --- mixture of Gaussian laws --- diffusion model --- transition densities --- re-service --- Strang–Marchuk splitting approach --- random delays --- nematode infection --- first-passage-time --- total variation distance --- forecast combinations --- products of primes --- discrete time stochastic model --- multiplicative noises --- slowly varying functions --- growth curves --- stochastic process --- loan interest rate regulation --- birth-death process --- non-Markovian queue --- catastrophes --- exogenous factors --- seasonal environment --- repairs --- proportional hazard rates --- structural breaks --- transient probabilities --- first passage time (FPT) --- bounds --- double-ended queues --- mixed Gaussian process --- stochastic order --- time between inspections --- busy period --- diffusion --- continuous-time Markov chains --- general bulk service --- time-non-homogeneous birth-death processes --- stand-by server --- reliability --- sensor networks --- random impulses --- scale family of distributions --- maximum likelihood estimation --- multi-state network --- totally positive of order 2 --- lognormal diffusion process --- fractional birth-death processes --- exact asymptotics --- stochastic orders --- time-non-homogeneous jump-diffusion processes --- asymptotic distribution --- inverse first-passage problem --- nonhomogeneous Poisson process --- two-dimensional signature --- multiple vacation --- first-passage time --- mean square stability --- fractional queues --- differential entropy --- random parameter matrices --- Wasserstein distance --- breakdown and repair --- fusion estimation
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