New developments in Functional and Fractional Differential Equations and in Lie Symmetry
Stavroulakis, Ioannis
New developments in Functional and Fractional Differential Equations and in Lie Symmetry - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021 - 1 electronic resource (155 p.)
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.
Creative Commons
English
books978-3-0365-1159-7 9783036511580 9783036511597
10.3390/books978-3-0365-1159-7 doi
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
New developments in Functional and Fractional Differential Equations and in Lie Symmetry - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021 - 1 electronic resource (155 p.)
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.
Creative Commons
English
books978-3-0365-1159-7 9783036511580 9783036511597
10.3390/books978-3-0365-1159-7 doi
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