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Fractional Order Systems

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ISBN: 9783039216086 9783039216093 Year: Pages: 114 DOI: 10.3390/books978-3-03921-609-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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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.

Fractional Differential Equations: Theory, Methods and Applications

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ISBN: 9783039217328 9783039217335 Year: Pages: 172 DOI: 10.3390/books978-3-03921-733-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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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.

Advanced Mathematical Methods: Theory and Applications

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ISBN: 9783039282463 9783039282470 Year: Pages: 198 DOI: 10.3390/books978-3-03928-247-0 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2020-04-07 23:07:08
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The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.

Keywords

ultraparabolic equation --- ultradiffusion process --- probabilistic representation --- mathematical finance --- linear elastostatics --- layer potentials --- fredholmian operators --- fractional differential equations --- fractional derivative --- Abel-type integral --- time delay --- distributed lag --- gamma distribution --- macroeconomics --- Keynesian model --- integral transforms --- Laplace integral transform --- transmutation operator --- generating operator --- integral equations --- differential equations --- operational calculus of Mikusinski type --- Mellin integral transform --- fractional derivative --- fractional integral --- Mittag–Leffler function --- Riemann–Liouville derivative --- Caputo derivative --- Grünwald–Letnikov derivative --- space-time fractional diffusion equation --- fractional Laplacian --- subordination principle --- Mittag-Leffler function --- Bessel function --- exterior calculus --- exterior algebra --- electromagnetism --- Maxwell equations --- differential forms --- tensor calculus --- Fourier Theory --- DFT in polar coordinates --- polar coordinates --- multidimensional DFT --- discrete Hankel Transform --- discrete Fourier Transform --- Orthogonality --- multispecies biofilm --- biosorption --- free boundary value problem --- heavy metals toxicity --- method of characteristics --- relativistic diffusion equation --- Caputo fractional derivatives of a function with respect to another function --- Bessel-Riesz motion --- Mittag–Leffler function --- matrix function --- Schur decomposition --- Laplace transform --- fractional calculus --- central limit theorem --- anomalous diffusion --- stable distribution --- fractional calculus --- power law --- n/a

Current Trends in Symmetric Polynomials with their Applications

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ISBN: 9783039216208 9783039216215 Year: Pages: 238 DOI: 10.3390/books978-3-03921-621-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Fubini polynomials --- w-torsion Fubini polynomials --- fermionic p-adic integrals --- symmetric identities --- Chebyshev polynomials --- sums of finite products --- hypergeometric function --- Fubini polynomials --- Euler numbers --- symmetric identities --- elementary method --- computational formula --- two variable q-Berstein polynomial --- two variable q-Berstein operator --- q-Euler number --- q-Euler polynomial --- Fubini polynomials --- Euler numbers --- congruence --- elementary method --- q-Bernoulli numbers --- q-Bernoulli polynomials --- two variable q-Bernstein polynomials --- two variable q-Bernstein operators --- p-adic integral on ?p --- the degenerate gamma function --- the modified degenerate gamma function --- the degenerate Laplace transform --- the modified degenerate Laplace transform --- Fibonacci --- Lucas --- linear form in logarithms --- continued fraction --- reduction method --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Hermite --- generalized Laguerre --- Legendre --- Gegenbauer --- Jacobi --- third-order character --- classical Gauss sums --- rational polynomials --- analytic method --- recursive formula --- fermionic p-adic q-integral on ?p --- q-Euler polynomials --- q-Changhee polynomials --- symmetry group --- Apostol-type Frobenius–Euler polynomials --- three-variable Hermite polynomials --- symmetric identities --- explicit relations --- operational connection --- q-Volkenborn integral on ?p --- Bernoulli numbers and polynomials --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- Changhee polynomials --- Changhee polynomials of type two --- fermionic p-adic integral on ?p --- Chebyshev polynomials of the first, second, third, and fourth kinds --- sums of finite products --- representation --- catalan numbers --- elementary and combinatorial methods --- recursive sequence --- convolution sums --- well-posedness --- stability --- acoustic wave equation --- perfectly matched layer --- Fibonacci polynomials --- Lucas polynomials --- trivariate Fibonacci polynomials --- trivariate Lucas polynomials --- generating functions --- central incomplete Bell polynomials --- central complete Bell polynomials --- central complete Bell numbers --- Legendre polynomials --- Laguerre polynomials --- generalized Laguerre polynomials --- Gegenbauer polynomials --- hypergeometric functions 1F1 and 2F1 --- Euler polynomials --- Bernoulli polynomials --- elementary method --- identity --- congruence --- new sequence --- Catalan numbers --- elementary and combinatorial methods --- congruence --- conjecture --- fluctuation theorem --- thermodynamics of information --- stochastic thermodynamics --- mutual information --- non-equilibrium free energy --- entropy production

Stochastic Processes: Theory and Applications

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ISBN: 9783039219629 9783039219636 Year: Pages: 216 DOI: 10.3390/books978-3-03921-963-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics --- Statistics
Added to DOAB on : 2020-01-07 09:08:26
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The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited to: Markov chains and processes; large deviations and limit theorems; random motions; stochastic biological model; reliability, availability, maintenance, inspection; queueing models; queueing network models; computational methods for stochastic models; applications to risk theory, insurance and mathematical finance.

Keywords

measure of information --- cumulative inaccuracy --- mutual information --- lower record values --- parabolic equation --- Cauchy problem --- Monte Carlo method --- unbiased estimator --- von-Neumann–Ulam scheme --- compound poisson insurance risk model --- expected discounted penalty function --- estimation --- Fourier transform --- Fourier-cosine series --- multidimensional birth-death process --- inhomogeneous continuous-time Markov chain --- rate of convergence --- one dimensional projection --- Wiener–Poisson risk model --- survival probability --- Nonparametric threshold estimation --- wet periods --- total precipitation volume --- asymptotic approximation --- extreme order statistics --- random sample size --- testing statistical hypotheses --- queueing systems --- rate of convergence --- non-stationary --- Markovian queueing models --- limiting characteristics --- queuing network --- retrials --- state-dependent marked Markovian arrival process --- wireless telecommunication networks --- time-dependent queue-length probability --- discrete-time Geo/D/1 queue --- closed-form solution --- Monte Carlo method --- quasi-Monte Carlo method --- Koksma-Hlawka inequality --- quasi-random sequences --- stochastic processes --- processor heating and cooling --- markovian arrival process --- phase-type service time distribution --- impatience --- Quasi-Birth-and-Death process --- matrix-geometric solution --- truncated distribution --- Markovian arrival process --- multi-class arrival processes --- product form --- equity-linked death benefits --- Fourier cosine series expansion --- guaranteed minimum death benefit --- option --- valuation --- Lévy process --- compound Poisson risk model --- generalized Gerber–Shiu discounted penalty function --- Laplace transform --- Dickson–Hipp operator --- recursive formula

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