New developments in Functional and Fractional Differential Equations and in Lie Symmetry
Stavroulakis, Ioannis (editor)
Jafari, H (editor)
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.
Keywordsintegro–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
Webshop linkhttps://mdpi.com/books/pdfview ...
Publication date and placeBasel, Switzerland, 2021
Research & information: general
Mathematics & science