The general solutions of difference vector-equations with constant coefficients by Artūras Štikonas

“…We find the simple formulae between solution of the first order homogeneous differential equations and solution of difference equation. …”
Get full text

Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators by Dumitru Baleanu, J. A. Tenreiro Machado, Carlo Cattani, Mihaela Cristina Baleanu, Xiao-Jun Yang

“…The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.…”
Get full text

Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System by Yang Zhao, De-Fu Cheng, Xiao-Jun Yang

“…The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.…”
Get full text

Modeling and Dynamical Behavior of Rotating Composite Shafts with SMA Wires by Yongsheng Ren, Qiyi Dai, Ruijun An, Youfeng Zhu

“…The equations of motion are derived based on the variational-asymptotical method (VAM) and Hamilton’s principle. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin method. …”
Get full text

Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System by M. Sheikholeslami, H. R. Ashorynejad, G. Domairry, I. Hashim

“…The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved analytically using the homotopy analysis method (HAM). …”
Get full text

Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. by Byonaneebye, Darius

“…The Dormand-Prince method is a technique similar to the Runge-Kutta method for solving ordinary differential equations (ODEs). It uses six function evaluations to compute solutions with fourth and fifth-order accuracy. …”
Get full text

A New Type of Distributed Parameter Control Systems: Two-Point Boundary Value Problems for Infinite-Dimensional Dynamical Systems by De-Xing Kong, Fa Wu

“…This survey note describes a new type of distributed parameter control systems—the two-point boundary value problems for infinite-dimensional dynamical systems, particularly, for hyperbolic systems of partial differential equations of second order, some of the discoveries that have been done about it and some unresolved questions.…”
Get full text

The shallow water equations: conservation laws and symplectic geometry by Yilmaz Akyildiz

“…We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. …”
Get full text

Some Generalized Gronwall-Bellman Type Impulsive Integral Inequalities and Their Applications by Yuzhen Mi

“…Our result is also applied to study a boundary value problem of differential equations with impulsive terms.…”
Get full text

Coincidence Fixed-Point Theorems for p-Hybrid Contraction Mappings in Gb-Metric Space with Application by Lucas Wangwe

“…Henceforth, the illustrative applications are given by using nonlinear fractional differential equations.…”
Get full text

Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate by Li Yingke, Chen Liang, Wang Kai

“…Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.…”
Get full text

On the Differential Operators with Periodic Matrix Coefficients by O. A. Veliev

“…We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. …”
Get full text

Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals by M. Tavassoli Kajani, S. Vahdati, Zulkifly Abbas, Mohammad Maleki

“…Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. …”
Get full text

Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets by Ai-Min Yang, Yu-Zhu Zhang, Carlo Cattani, Gong-Nan Xie, Mohammad Mehdi Rashidi, Yi-Jun Zhou, Xiao-Jun Yang

“…The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.…”
Get full text

Positive Solutions for Nonlinear Singular Differential Systems Involving Parameter on the Half-Line by Lishan Liu, Ying Wang, Xinan Hao, Yonghong Wu

“…By using the upper-lower solutions method and the fixed-point theorem on cone in a special space, we study the singular boundary value problem for systems of nonlinear second-order differential equations involving two parameters on the half-line. …”
Get full text

Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay by Bo Zhu, Minhui Zhu

“…An example involving partial differential equations with noninstantaneous impulses is given to show the application of our main results.…”
Get full text

C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems by Congcong Shen, Lining Jiang, Zhenhua Ma

“…As an application, we prove the existence and uniqueness of the solution of a type of differential equations.…”
Get full text

Exact Traveling Wave Solutions to the (2 + 1)-Dimensional Jaulent-Miodek Equation by Yongyi Gu, Bingmao Deng, Jianming Lin

“…It has presented that the applied method is very efficient and is practically well suited for the nonlinear differential equations that arise in mathematical physics.…”
Get full text

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1:1:1 Simultaneous Resonance by Ali Kandil, Y. S. Hamed, Jan Awrejcewicz, Nasser A. Saeed

“…These deflections are governed by a system of two ordinary differential equations in order to describe their Cartesian directions. …”
Get full text

A Numerical Assessment of Time-Dependent Magneto-Convective Thermal-Material Transfer over a Vertical Permeable Plate by Mohammed Jahir Uddin, R. Nasrin

“…The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. …”
Get full text