Applications of alternative problems

Solution to equations in function space relating linear operator defined in subspace of Banach space and linear or nonlinear operato

Continuous dependence of fixed points of condensing maps

Many problems in analysis are concerned with the dependence upon parameters of fixed points of maps. For contraction mappings, criteria are relatively easy to obtain and have been known for some time. In the study of solutions of functional differential equations, more general results were needed. It is the purpose of this paper to give a rather general fixed-point theorem for condensing maps depending on a parameter, to prove continuous dependence and to indicate how many of the previous results are special cases

Behavior near a periodic orbit of functional differential equations

Behavior near periodic orbit of functional differential equation

Functional differential equations

Functional class of differential-difference, retard differential, and difference equation

A Class of Linear Functional Equations

Summary on autonomous linear functional equation

Averaging methods for differential equations with retarded arguments and a small parameter

Differential equations with retarded arguments and small paramete

A Survey of Some Current Research in Functional-differential Equations

Functional differential equation applications using geometric approac

A Class of Functional Equations of Neutral Type

Class of functional integral equations in space of continuous function

An efficient implementation of an implicit FEM scheme for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a modelling tool for processes with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues, which impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids, and robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analysing the speed of the travelling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator