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Operators of Fractional Calculus and Their Applications

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ISBN: 9783038973409 / 9783038973416 Year: Pages: 136 DOI: 10.3390/books978-3-03897-341-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Physics (General)
Added to DOAB on : 2019-01-16 12:17:12
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During the past four decades or so, various operators of fractional calculus, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdelyi–Kober, Liouville–Caputo, and so on, have been found to be remarkably popular and important due mainly to their demonstrated applications in numerous diverse and widespread fields of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional calculus operators provide several potentially useful tools for solving differential, integral, differintegral, and integro-differential equations, together with the fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, as well as their extensions and generalizations in one and more variables. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional calculus and its multidisciplinary applications.

Advanced Numerical Methods in Applied Sciences

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ISBN: 9783038976660 / 9783038976677 Year: Pages: 306 DOI: 10.3390/books978-3-03897-667-7 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 08:44:06
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

Keywords

time fractional differential equations --- mixed-index problems --- analytical solution --- asymptotic stability --- conservative problems --- Hamiltonian problems --- energy-conserving methods --- Poisson problems --- Hamiltonian Boundary Value Methods --- HBVMs --- line integral methods --- constrained Hamiltonian problems --- Hamiltonian PDEs --- highly oscillatory problems --- boundary element method --- finite difference method --- floating strike Asian options --- continuous geometric average --- barrier options --- isogeometric analysis --- adaptive methods --- hierarchical splines --- THB-splines --- local refinement --- linear systems --- preconditioners --- Cholesky factorization --- limited memory --- Volterra integral equations --- Volterra integro–differential equations --- collocation methods --- multistep methods --- convergence --- B-spline --- optimal basis --- fractional derivative --- Galerkin method --- collocation method --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- discretization of systems of differential equations --- higher-order finite element methods --- discontinuous Galerkin methods --- finite difference methods --- isogeometric analysis --- B-splines --- curl–curl operator --- time harmonic Maxwell’s equations and magnetostatic problems --- low rank completion --- matrix ODEs --- gradient system --- ordinary differential equations --- Runge–Kutta --- tree --- stump --- order --- elementary differential --- edge-histogram --- edge-preserving smoothing --- histogram specification --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods --- hyperbolic partial differential equations --- high order discontinuous Galerkin finite element schemes --- shock waves and discontinuities --- vectorization and parallelization --- high performance computing --- generalized Schur algorithm --- null-space --- displacement rank --- structured matrices --- stochastic differential equations --- stochastic multistep methods --- stochastic Volterra integral equations --- mean-square stability --- asymptotic stability --- numerical analysis --- numerical methods --- scientific computing --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods

Stochastic Processes with Applications

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ISBN: 9783039217281 / 9783039217298 Year: Pages: 284 DOI: 10.3390/books978-3-03921-729-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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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.

Keywords

fusion estimation --- sensor networks --- random parameter matrices --- multiplicative noises --- random delays --- realized volatility --- forecast combinations --- structural breaks --- arithmetic progressions --- first Chebyshev function --- products of primes --- regularly varying functions --- slowly varying functions --- mixed Gaussian process --- small deviations --- exact asymptotics --- loan interest rate regulation --- diffusion model --- first passage time (FPT) --- continuous-time Markov chains --- catastrophes --- bounds --- birth-death process --- rate of convergence --- double-ended queues --- time-non-homogeneous birth-death processes --- catastrophes --- repairs --- transient probabilities --- periodic intensity functions --- time-non-homogeneous jump-diffusion processes --- transition densities --- first-passage-time --- lognormal diffusion process --- exogenous factors --- growth curves --- maximum likelihood estimation --- asymptotic distribution --- first-passage time --- inverse first-passage problem --- diffusion --- mixture of Gaussian laws --- rate of convergence --- total variation distance --- Wasserstein distance --- weighted quadratic variation --- non-Markovian queue --- general bulk service --- multiple vacation --- breakdown and repair --- stand-by server --- re-service --- discrete time stochastic model --- first-passage time --- time between inspections --- host-parasite interaction --- nematode infection --- nonhomogeneous Poisson process --- seasonal environment --- Strang–Marchuk splitting approach --- Cohen and Grossberg neural networks --- random impulses --- mean square stability --- fractional differential-difference equations --- fractional queues --- fractional birth-death processes --- busy period --- two-dimensional signature --- multi-state network --- totally positive of order 2 --- stochastic order --- stochastic process --- reliability --- stochastic orders --- scale family of distributions --- proportional hazard rates --- differential entropy

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2019 (3)