Natural vibrations and instability of plane frames: Exact analytical solutions using power series

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

Download Full-text

Exact analytical solutions for forced cubic restoring force oscillator

Nonlinear Dynamics ◽

10.1007/s11071-015-2486-2 ◽

2015 ◽

Vol 83 (4) ◽

pp. 2349-2359 ◽

Cited By ~ 2

Author(s):

Uwe Starossek

Keyword(s):

Analytical Solutions ◽

Restoring Force ◽

Exact Analytical Solutions

Download Full-text

Modelling Activity and Durability of Electrocatalysts from a Statistical Perspective

10.26434/chemrxiv.14075900 ◽

2021 ◽

Author(s):

Jun Huang

Keyword(s):

Exponential Decay ◽

Analytical Solutions ◽

Electrocatalytic Activity ◽

Active Sites ◽

Simple Theory ◽

Exact Analytical Solutions ◽

Modelling Activity ◽

Closing The Gap ◽

The Mean ◽

Kinetics Of

<p>We develop a theory to investigate how energetic nonhomogeneity of active sites determines the overall activity of an electrocatalyst and how the evolution of the nonhomogeneity determines the overall durability. The simple theory is amenable to exact analytical solutions and thus fosters an in-depth transparent analysis. It is revealed that nonhomogeneity does not necessarily diminish the electrocatalytic activity; instead, the highest overall activity is obtained with a suitable level of nonhomogeneity that is commensurate with the mean property. The evolution kinetics of nonhomogeneity is described by using the Fokker-Planck theory. Exponential decay of the activity is predicted theoretically and confirmed experimentally. The present work represents a first step toward closing the gap between model and practical electrocatalysts using statistical considerations.</p>

Download Full-text

INFLATIONARY SCENARIO IN BRANS–DICKE THEORY FOR BIANCHI VI0 SPACE–TIME MODEL

International Journal of Modern Physics D ◽

10.1142/s0218271803002421 ◽

2003 ◽

Vol 12 (01) ◽

pp. 129-143 ◽

Cited By ~ 1

Author(s):

SUBENOY CHAKRABORTY ◽

ARABINDA GHOSH

Keyword(s):

Equation Of State ◽

Perfect Fluid ◽

Analytical Solutions ◽

Fluid Model ◽

Space Time ◽

Time Model ◽

Exact Analytical Solutions ◽

Exponential Expansion ◽

Barotropic Equation ◽

Space Time Model

We have investigated perfect fluid model in Brans–Dicke theory for Bianchi VI 0 space–time and have obtained exact analytical solutions considering barotropic equation of state. These solutions have been analyzed for different values of the parameters involved and some of them have shown a period of exponential expansion.

Download Full-text

Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

Abstract and Applied Analysis ◽

10.1155/2012/426514 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Adel Al-Rabtah ◽

Shaher Momani ◽

Mohamed A. Ramadan

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Fractional Differential Equations ◽

Analytical Solutions ◽

Spline Functions ◽

Exact Analytical Solutions ◽

Nonlinear Fractional Differential Equations ◽

Fractional Differential ◽

Linear And Nonlinear ◽

Good Agreement

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for0<α≤1andα≥1, whereαdenotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.

Download Full-text