New Developments in Functional and Fractional Differential Equations and in Lie Symmetry

<p>Delay difference functional fractional and partial differential equations have many applications in science and engineering. In this Special Issue 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows:</p><p>Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in <em>Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays</em> whereas a sharp oscillation criterion using the notion of slowly varying functions is established in <em>A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay</em>. The approximation of a linear autonomous differential equation with a small delay is considered in <em>Approximation of a Linear Autonomous Differential Equation with Small Delay</em>; the model of infection diseases by Marchuk is studied in <em>Around the Model of Infection Disease: The Cauchy Matrix and Its Properties</em>. </p><p>Exact solutions to fractional-order Fokker-Planck equations are presented in <em>New Exact Solutions and Conservation Laws to the Fractional-Order Fokker-Planck Equations</em> and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in <em>A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise</em>. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in <em>Finite Difference Approximation Method for a Space Fractional Convection-Diffusion Equation with Variable Coefficients</em>; existence results for a nonlinear fractional difference equation with delay and impulses are established in <em>On Nonlinear Fractional Difference Equation with Delay and Impulses</em>. </p><p>A complete Noether symmetry analysis of a generalized coupled Lane-Emden-Klein-Gordon-Fock system with central symmetry is provided in <em>Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays</em> and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in <em>New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis.</em></p>