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

Research & information: general --- Mathematics & science --- integro–differential systems --- Cauchy matrix --- exponential stability --- distributed control --- delay differential equation --- ordinary differential equation --- asymptotic equivalence --- approximation --- eigenvalue --- oscillation --- variable delay --- deviating argument --- non-monotone argument --- slowly varying function --- Crank–Nicolson scheme --- Shifted Grünwald–Letnikov approximation --- space fractional convection-diffusion model --- variable coefficients --- stability analysis --- Lane-Emden-Klein-Gordon-Fock system with central symmetry --- Noether symmetries --- conservation laws --- differential equations --- non-monotone delays --- fractional calculus --- stochastic heat equation --- additive noise --- chebyshev polynomials of sixth kind --- error estimate --- fractional difference equations --- delay --- impulses --- existence --- fractional Jaulent-Miodek (JM) system --- fractional logistic function method --- symmetry analysis --- lie point symmetry analysis --- approximate conservation laws --- approximate nonlinear self-adjointness --- perturbed fractional differential equations --- integro–differential systems --- Cauchy matrix --- exponential stability --- distributed control --- delay differential equation --- ordinary differential equation --- asymptotic equivalence --- approximation --- eigenvalue --- oscillation --- variable delay --- deviating argument --- non-monotone argument --- slowly varying function --- Crank–Nicolson scheme --- Shifted Grünwald–Letnikov approximation --- space fractional convection-diffusion model --- variable coefficients --- stability analysis --- Lane-Emden-Klein-Gordon-Fock system with central symmetry --- Noether symmetries --- conservation laws --- differential equations --- non-monotone delays --- fractional calculus --- stochastic heat equation --- additive noise --- chebyshev polynomials of sixth kind --- error estimate --- fractional difference equations --- delay --- impulses --- existence --- fractional Jaulent-Miodek (JM) system --- fractional logistic function method --- symmetry analysis --- lie point symmetry analysis --- approximate conservation laws --- approximate nonlinear self-adjointness --- perturbed fractional differential equations