This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

The nonlinear discrete-time optimal control problem with terminal constraints is treated using a new evolutionary approach which combines a genetic search for finding the control sequence with a solution of the initial value problem for the state variables. The main advantage of the method is that it does not require to obtain the solution of the adjoint problem which usually leads to a two-poi...

In this article, we consider a single-phase coupled nonlinear Stefan problem of the water-head and concentration equations with nonlinear source and permeance terms and a Dirichlet boundary condition depending on the free-boundary function. The problem is very important in subsurface contaminant transport and remediation, seawater intrusion and control, and many other applications. While a Land...

The nonlinear two-point boundary value problem occurs quite naturally in studies in many diverse science branches. For obtaining the approaching solution of the nonlinear problem we often replace the nonlinear problem with a sequence of linear problems in such a manner that the sequence of solutions to the linear problems approach in a limiting sense the solution of the nonlinear problem. The c...

Abstract This paper is devoted to a game-theoretic approach the level-set curvature flow equation with nonlinear dynamic boundary conditions. Under comparison principle for problem, we construct family of deterministic discrete games, whose value functions approximate unique viscosity solution. We also apply game approximation study convexity preserving properties and fattening phenomenon this ...