Reprint

Fractional Differential Equations

Theory, Methods and Applications

Edited by
November 2019
172 pages
  • ISBN978-3-03921-732-8 (Paperback)
  • ISBN978-3-03921-733-5 (PDF)

This book is a reprint of the Special Issue Fractional Differential Equations: Theory, Methods and Applications that was published in

Biology & Life Sciences
Chemistry & Materials Science
Computer Science & Mathematics
Physical Sciences
Summary

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.

Format
  • Paperback
License
© 2020 by the authors; CC BY license
Keywords
fractional q-difference equation; existence and uniqueness; positive solutions; fixed point theorem on mixed monotone operators; fractional p-Laplacian; Kirchhoff-type equations; fountain theorem; modified functional methods; Moser iteration method; fractional-order neural networks; delays; distributed delays; impulses; Mittag–Leffler synchronization; Lyapunov functions; Razumikhin method; generalized convexity; b-vex functions; sub-b-s-convex functions; oscillation; nonlinear differential system; delay differential system; α-fractional derivative; positive solution; fractional thermostat model; fixed point index; dependence on a parameter; Hermite–Hadamard’s Inequality; Convex Functions; Power-mean Inequality; Jenson Integral Inequality; Riemann—Liouville Fractional Integration; Laplace Adomian Decomposition Method (LADM); Navier-Stokes equation; Caputo Operator; fractional-order system; model order reduction; controllability and observability Gramians; energy inequality; integral conditions; fractional wave equation; existence and uniqueness; initial boundary value problem; conformable fractional derivative; conformable partial fractional derivative; conformable double Laplace decomposition method; conformable Laplace transform; singular one dimensional coupled Burgers’ equation