Fractional-in-Time Semilinear Parabolic Equations and Applications
Publication Date: 2020
ISBN: 978-3-030-45043-4
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This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics.
Subject: Mathematics and Statistics, Partial Differential Equations, Applications of Mathematics, Mathematical Methods in Physics, Semilinear parabolic equations, Caputo fractional derivative, Anomalous diffusion, Fractional Laplace operator, Existence and regularity of solutions, Reaction-diffusion systems, Fractional in time equations, Fractional Brownian motion, Lévy flight, Schneider-Grey Brownian motion
