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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.
fractional wave equation --- dependence on a parameter --- conformable double Laplace decomposition method --- Riemann—Liouville Fractional Integration --- Lyapunov functions --- Power-mean Inequality --- modified functional methods --- oscillation --- fractional-order neural networks --- initial boundary value problem --- fractional p-Laplacian --- model order reduction --- ?-fractional derivative --- Convex Functions --- existence and uniqueness --- conformable partial fractional derivative --- nonlinear differential system --- conformable Laplace transform --- Mittag–Leffler synchronization --- delays --- controllability and observability Gramians --- impulses --- conformable fractional derivative --- Moser iteration method --- fractional q-difference equation --- energy inequality --- b-vex functions --- Navier-Stokes equation --- fractional-order system --- Kirchhoff-type equations --- Razumikhin method --- Laplace Adomian Decomposition Method (LADM) --- fountain theorem --- Hermite–Hadamard’s Inequality --- distributed delays --- Caputo Operator --- fractional thermostat model --- sub-b-s-convex functions --- fixed point theorem on mixed monotone operators --- singular one dimensional coupled Burgers’ equation --- generalized convexity --- delay differential system --- positive solutions --- positive solution --- fixed point index --- Jenson Integral Inequality --- integral conditions
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This book is devoted to Prof. Juan J. Nieto, on the occasion of his 60th birthday. Juan José Nieto Roig (born 1958, A Coruña) is a Spanish mathematician, who has been a Professor of Mathematical Analysis at the University of Santiago de Compostela since 1991. His most influential contributions to date are in the area of differential equations. Nieto received his degree in Mathematics from the University of Santiago de Compostela in 1980. He was then awarded a Fulbright scholarship and moved to the University of Texas at Arlington where he worked with Professor V. Lakshmikantham. He received his Ph.D. in Mathematics from the University of Santiago de Compostela in 1983. Nieto's work may be considered to fall within the ambit of differential equations, and his research interests include fractional calculus, fuzzy equations and epidemiological models. He is one of the world’s most cited mathematicians according to Web of Knowledge, and appears in the Thompson Reuters Highly Cited Researchers list. Nieto has also occupied different positions at the University of Santiago de Compostela, such as Dean of Mathematics and Director of the Mathematical Institute. He has also served as an editor for various mathematical journals, and was the editor-in-chief of the journal Nonlinear Analysis: Real World Applications from 2009 to 2012. In 2016, Nieto was admitted as a Fellow of the Royal Galician Academy of Sciences. This book consists of contributions presented at the International Conference on Nonlinear Analysis and Boundary Value Problems, held in Santiago de Compostela, Spain, 4th-7th September 2018. Covering a variety of topics linked to Nieto’s scientific work, ranging from differential, difference and fractional equations to epidemiological models and dynamical systems and their applications, it is primarily intended for researchers involved in nonlinear analysis and boundary value problems in a broad sense. .
Differential Equations. --- Differential equations, partial. --- Functional equations. --- Differentiable dynamical systems. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Difference and Functional Equations. --- Dynamical Systems and Ergodic Theory. --- Mathematical and Computational Biology. --- Mathematical Applications in the Physical Sciences. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations --- 517.91 Differential equations --- Equations, Functional --- Functional analysis --- Boundary value problems --- Differential equations. --- Partial differential equations. --- Difference equations. --- Dynamics. --- Ergodic theory. --- Biomathematics. --- Mathematical physics. --- Physical mathematics --- Physics --- Biology --- Mathematics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Calculus of differences --- Differences, Calculus of --- Equations, Difference
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