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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 stateoftheart of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.
ultraparabolic equation  ultradiffusion process  probabilistic representation  mathematical finance  linear elastostatics  layer potentials  fredholmian operators  fractional differential equations  fractional derivative  Abeltype 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  spacetime fractional diffusion equation  fractional Laplacian  subordination principle  MittagLeffler 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  BesselRiesz 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
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