Peskin’s Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L∞ norm. But almost none rigorous proof could be foun...

In this paper, we study periodic boundary value problems for a class of linear fractional evolution equations involving the Caputo fractional derivative. Utilizing compactness of the constructed evolution operators and Fredholm alternative theorem, some interesting alternative results for the mild solutions are presented. Periodic motion controllers that are robust to parameter drift are also d...

In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...

Abstract. We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after truncation to a finite interval, and we reformulate these problems as functional differential equations over a bounded domain. Connecting orbits are computed for sever...

Results of electro-thermo-elastic analysis of a functionally graded thick-walled spherical shell made of temperature dependent materials are presented in this article. All material properties are assumed temperature-dependent and also are graded along the thickness direction based on power function. Temperature dependency is accounted for all material properties including, thermal, mechanical a...

This paper presents a general formulation to investigate the scattering from Multilayer Lossy Inhomogeneous Metamaterial Planar Structure (MLIMPS) with arbitrary number of layers and polarization. First, the dominating differential equation of transverse components of electromagnetic fields in each layers derived. Considering the general form of solution of the differential equations and the bo...

In this paper, new estimates of the sequential Caputo fractional derivatives a function at its extremum points are obtained.We derive comparison principles for linear differential equations, then apply these to obtain lower and upper bounds solutions nonlinear equations. The principle is applied show that initial-boundary-value problem anomalous diffusion admits most one classical solution depe...

‎the problem of two-phase mhd boundary layer flow, heat and mass transfer over a stretching sheet with fluid-particle suspension and thermal radiation has been studied. the effect of mass transfer in dusty fluid over a stretching sheet is considered for the first time. the governing equations are reduced to a set of non-linear ordinary differential equations under suitable similarity transforma...

This paper considers a boundary feedback control problem for a MIMO counter-propagating Raman amplifier. The system is modeled as a set of coupled semilinear hyperbolic partial differential equations with Lotka-Volterra type nonlinearity. The system is linearized about the steady-state solution, and a boundary controller is designed based on a Lyapunov functional whose time derivative is made s...