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

• Format: eBook
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021
• Subjects: Mathematics & science; Research & information: general; additive noise; approximate conservation laws; approximate nonlinear self-adjointness; approximation; asymptotic equivalence; Cauchy matrix; chebyshev polynomials of sixth kind; conservation laws; Crank-Nicolson scheme; delay; delay differential equation; deviating argument; differential equations; distributed control; eigenvalue; error estimate; existence; exponential stability; fractional calculus; fractional difference equations; fractional Jaulent-Miodek (JM) system; fractional logistic function method; impulses; integro-differential systems; Lane-Emden-Klein-Gordon-Fock system with central symmetry; lie point symmetry analysis; Noether symmetries; non-monotone argument; non-monotone delays; ordinary differential equation; oscillation; perturbed fractional differential equations; Shifted Grünwald-Letnikov approximation; slowly varying function; space fractional convection-diffusion model; stability analysis; stochastic heat equation; symmetry analysis; variable coefficients; variable delay
• Online Access: Open Access: DOAB: description of the publication; Open Access: DOAB, download the publication
• Physical Description: 1 online resource (155 p.)
• ISBN: 9783036511580; 9783036511597; books978-3-0365-1159-7
• Access: Open Access

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.