This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

Table of Contents:
On the existence of positive solutions for the time-scale dynamic equations on infinite intervals (Dogan).- A randomized quasi-Monte Carlo algorithms for some boundary value problems (Sipin).- On the study of forward Kolmogorov system and the corresponding problems for inhomogeneous continuous-time Markov chains (Zeifman).- Convergence rate estimates for some models of queuing theory, and their applications (Zeifman et al.).- On Enlarged Sufficient Conditions for L2-Dissipativity of Linearized Explicit Schemes with Regularization for 1D Gas Dynamics Systems of Equations (Zlotnik).- Equilibrium of a linearly elastic body under generalized boundary data (Starita et al.).- Nonlocal problems for the fourth order impulsive partial differential equations (Assanova et al.).- Application of method of differential inequalities to bounding the rate of convergence for a class of Markov chains (Kryukova et al.).- The method of fractional steps for the numerical solution of a multidimensional heat conduction equation with delay for the case of variable coefficient of heat conductivity (Lekomtsev).- Hyers-Ulam stability of a nonlinear Volterra integral equation on time scales (Christian et al.).-The method of fractional steps for the numerical solution of a multidimensional heat conduction equation with delay for the case of variable coefficient of heat conductivity (Lekomtsev).- Hyers-Ulam stability of a nonlinear Volterra integral equation on time scales (Reinfelds et al.).- On some stochastic algorithms for the numerical solution of the first boundary value problem for the heat equation (Sipin et al.).- Local controllability of a class of fractional differential inclusions via derived cones (Aurelian).- A Modified Second-Order Collatz Equation as a Mathematical Model of Bipolar Disorder (Kent).- Local bifurcations in the generalized Cahn-Hilliard equation (Kulikovet et al.).- The numerical solution of wave equation with delay for the case of variable velocity coefficient (Tashirova).- Two nontrivial solutions for Robin problems driven by a p−Laplacian operator (Aguı et al.).- Multiple periodic solutions for a Duffing type equation with one-sided sublinear nonlinearity: Beyond the Poincare-Birkhoff twist theorem (Donde` et al.).- Dynamical models of interrelation in a class of artificial networks (Sadyrbaev et al.).- Analytic traveling-wave solutions of the Kardar-Parisi-Zhang interface growing equation with different kind of noise terms (Barna et al.).- Triple solutions for elastic beam equations of the fourth-order with boundary conditions subjected to an elastic device (Bonanno et al.).- Dynamics of discrete operator equations (Karakostas).- Research of four-dimensional dynamic systems describing processes of three’level assimilation (Chilachava et al.).- Two positive solutions for a nonlinear Neuman problem involving the discrete p−Laplacian (Bonanno et al.).- Structure of solution sets for fractional partial integro-differential equations (Benaouda).- Study of the Equivalent Impedance Of A Resonator Array Using Difference Equations (Albuquerque et al.).-Asymptotics of an Equation with Large State-Dependent Delay (Kashchenko).- About Some Methods of Analytic Representation and Classfication of a Wide Set of Geometric Figures with "Complex" Configuration (Tavkhelidze et al.).- On nonpower-law asymptotic behavior of blow-up solutions to Emden-Fowler type higher-order differential equations (Astashova et al.).- Third Order Iterative Method for Nonlinear Difference Schemes (Iumanova et al.).- Non-homogeneous boundary problems for one-dimensional flow of the compressible viscous and heat-conducting micropolar fluid (Draˇzic´).- The general case of cutting GML bodies (Gielis).- Computational simulation of bacterial infections in surgical procedures: an exploratory study (Ferreira et al.).- Coupling temperature with drug diffusion: a second order approximation (Ferreira et al.).- Drug release from thermosensitive polymeric platforms - towards non Fickian models (Ferreira et al.).- Some properties of a generalized solution for shear flow of a compressible viscous micropolar fluid model (Simˇcic´).- Collocation solution of fractional differential equations in piecewise nonpolynomial spaces (Lu´ısa et al.).- On conditions on the potential in a Sturm– Liouville problem and an upper estimate of its first eigenvalue (Ezhak et al.).- IFOHAM-a generalization of the Picard-Lindel off iteration method (Sacramento et al.).- Well-Posedness of Volterra Integro-differential Equations with Fractional Exponential Kernels (Rautian).- On non-local boundary-value problems fo higher-order non-linear functional differential equations (Dilna).- On the discrete Fourier transform eigenvectors and spontaneous symmetry breaking (Atakishiyeva et al.).- General sets of Bell-Sheffer and Log-Sheffer polynomials (Natalini et al.).- Existence results for periodic boundary value problems with a convenction term (Candito et al.).- Numerical Solution of the Time Fractional Cable Equation (Morgado et al.).- Modelling Antibody-Antigen Interactions (Wang).- Positive solutions for a class of nonlocal discrete boundary value problems (Luca).- Dynamics of a certain nonlinearly perturbed heat equation (Ramos).- The dynamics of a hybrid chaotic system (Ramos et al.).- On regularity of tetrahedral meshes produced by some red-type refinements (Korotov et al.).- Difference scheme for partial differential equations of fractional order with a nonlinear differentiation operator (Solodushkin et al.).- On the behavior of solutions with positive initial data to higher-order differential equations with general power-law noninearity (Korchemkina et al.).- Intuitionistic Fuzzy Stability of an Finite Dimesnional Cubic Functional Equation (Pinelas).- An Abstract Impulsive Second-Order Functional-Differential Cauchy Problems with Nonlocal Conditions (Akca).- Representations of solutions of hyperbolic Volterra integro-differential equations with singular kernels (Vlasov et al.).- Chiral properties of discrete Joyce and Hestenes equations (Sushch).