Numerical simulation of the nonlinear generalized time‐fractional Klein–Gordon equation using cubic trigonometric B‐spline functions

In this paper, an efficient numerical procedure for the generalized nonlinear time‐fractional Klein–Gordon equation is presented. We make use of the typical finite difference schemes to approximate the Caputo time‐fractional derivative, while the spatial derivatives are discretized by means of the cubic trigonometric B‐splines. Stability and convergence analysis for the numerical scheme are discussed. We apply our scheme to some typical examples and compare the obtained results with the ones found by other numerical methods. The comparison shows that our scheme is quite accurate and can be applied successfully to a variety of problems of applied nature.     

A study of higher-order nonlinear ordinary differential equations with four-point nonlocal integral boundary conditions

This paper investigates some new existence results for an nth-order nonlinear differential equation with four-point nonlocal integral boundary conditions (strip/slit like conditions). Our results are based on some standard fixed point theorems and Leray-Schauder degree theory.     

Effect of Pd Concentration on the Structure and Physical Properties of Ag100 – xPdx (x = 40, 50, and 60 at %) Alloys

Physics of the Solid State - Experimental investigations have been carried out to study the effect of Pd on the structure and physical properties of binary Ag100 – xPdx (at...     

New predictor-corrector approach for nonlinear fractional differential equations: error analysis and stability

In this paper, the predictor-corrector approach is used to propose two algorithms for the numerical solution of linear and non-linear fractional differential equations (FDE). The fractional order derivative is taken to be in the sense of Caputo and its properties are used to transform FDE into a Volterra-type integral equation. Simpson''s 3/8 rule is used to develop new numerical schemes to obtain the approximate solution of the integral equation associated with the given FDE. The error and stability analysis for the two methods are presented. The proposed methods are compared with the ones available in the literature. Numerical simulation is performed to demonstrate the validity and applicability of both the proposed techniques. As an application, the problem of dynamics of the new fractional order non-linear chaotic system introduced by Bhalekar and Daftardar-Gejji is investigated by means of the obtained numerical algorithms.     

Dynamics of a hepatitis B model with saturated incidence

In this article, we present a hepatitis B epidemic model with saturated incidence. The dynamic behaviors of the deterministic and stochastic system are studied. To this end, we first establish the local and global stability conditions of the equilibrium of the deterministic model. Second, by constructing suitable stochastic Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution as well as extinction of hepatitis B are obtained.     

Numerical solution of fourth-order time-fractional partial differential equations with variable coefficients

In this paper, a numerical method for fourth-order time-fractional partial differential equations with variable coefficients is proposed. Our method consists of Laplace transform, the homotopy perturbation method and Stehfest's numerical inversion algorithm. We show the validity and efficiency of the proposed method (so called LHPM) by applying it to some examples and comparing the results obtained by this method with the ones found by Adomian decomposition method (ADM) and He's variational iteration method (HVIM).     

Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type

We discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. The main tool of study is the monotone iterative technique.     

Covers and Directed Colimits

We find conditions on , a class of objects of a Grothendieck category, sufficient for the existence of -covers. The theory includes the existence of flat covers of modules.