05165nam 2200853z- 450 991055755180332120231214133147.0(CKB)5400000000044088(oapen)https://directory.doabooks.org/handle/20.500.12854/76706(EXLCZ)99540000000004408820202201d2021 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierNew developments in Functional and Fractional Differential Equations and in Lie SymmetryBasel, SwitzerlandMDPI - Multidisciplinary Digital Publishing Institute20211 electronic resource (155 p.)3-0365-1158-X 3-0365-1159-8 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: generalbicsscMathematics & sciencebicsscintegro–differential systemsCauchy matrixexponential stabilitydistributed controldelay differential equationordinary differential equationasymptotic equivalenceapproximationeigenvalueoscillationvariable delaydeviating argumentnon-monotone argumentslowly varying functionCrank–Nicolson schemeShifted Grünwald–Letnikov approximationspace fractional convection-diffusion modelvariable coefficientsstability analysisLane-Emden-Klein-Gordon-Fock system with central symmetryNoether symmetriesconservation lawsdifferential equationsnon-monotone delaysfractional calculusstochastic heat equationadditive noisechebyshev polynomials of sixth kinderror estimatefractional difference equationsdelayimpulsesexistencefractional Jaulent-Miodek (JM) systemfractional logistic function methodsymmetry analysislie point symmetry analysisapproximate conservation lawsapproximate nonlinear self-adjointnessperturbed fractional differential equationsResearch & information: generalMathematics & scienceStavroulakis Ioannisedt1323475Jafari HedtStavroulakis IoannisothJafari HothBOOK9910557551803321New developments in Functional and Fractional Differential Equations and in Lie Symmetry3035598UNINA