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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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Abstract

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

Mathematical Analysis and Applications II

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ISBN: 9783039283842 9783039283859 Year: Pages: 226 DOI: 10.3390/books978-3-03928-385-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:09
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Abstract

This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications” . Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.

Keywords

common fixed point --- metric-like space --- ?-Geraghty contraction --- triangular ?-admissible mapping --- fixed circle --- common fixed circle --- fixed-circle theorem --- extended partial Sb-metric spaces --- Sb-metric spaces --- fixed point --- generalized hypergeometric functions --- Gauss and confluent hypergeometric functions --- summation theorems of hypergeometric functions --- partial symmetric --- fixed point --- contraction and weak contraction --- Nadler’s theorem --- linear elastostatics --- simple layer potentials --- displacement problem --- existence and uniqueness theorems --- Fredholm alternative --- singular data --- differential equations --- Sheffer polynomial sets --- generating functions --- monomiality principle --- quasi metric space --- Suzuki contractions --- fixed point theorems --- modified ?-distance --- almost perfect functions --- generating function --- series transformation --- gamma function --- Hankel contour --- Fermi–Dirac function --- Bose–Einstein function --- Weyl transform --- series representation --- Hermite–Hadamard inequalities --- (p, q)-derivative --- (p, q)-integral --- convex functions --- fixed point --- Reich contraction --- Hardy–Rogers contraction --- almost b-metric space --- additive (Cauchy) equation --- additive mapping --- Hyers–Ulam stability --- generalized Hyers–Ulam stability --- hyperstability --- bounded index --- bounded L-index in direction --- slice function --- entire function --- bounded l-index --- generalized hypergeometric functions --- classical summation theorems --- generalization --- laplace transforms --- gamma and beta functions --- Szász-Mirakjan operators --- Szász-Mirakjan Beta type operators --- extended Gamma and Beta functions --- confluent hypergeometric function --- Modulus of smoothness --- modulus of continuity --- Lipschitz class --- local approximation --- Voronovskaja type approximation theorem --- operators theory 44A99, 47B99, 47A62 --- special functions 33C52, 33C65, 33C99, 33B10, 33B15 --- Stirling numbers and Touchard polynomials 11B73 --- n/a

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2020 (2)