A numerical approach for analyzing the transverse vibrations of an axially moving viscoelastic string

2014 ◽  
Vol 05 (03) ◽  
pp. 1450005
Author(s):  
Ying Wu ◽  
Weijia Zhao ◽  
Jiang Zhu
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Memory Effect ◽  
Dynamical Behavior ◽  
Numerical Approach ◽  
Computation Cost ◽  
Viscoelastic Parameters ◽  
Transverse Vibrations ◽  
Fractional Differential ◽  
Axially Moving

In this paper, a fractional differential equation is introduced to describe the transverse vibrations of an axially moving viscoelastic string. An iterative algorithm is constructed to analyze the dynamical behavior. By conveying the memory effect of the fractional differential terms step by step, the computation cost can be greatly reduced. As a numerical example, the effects of the viscoelastic parameters on a moving string are investigated.

scholarly journals On a fractional problem of Lane–Emden type: Ulam type stabilities and numerical behaviors

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kamel Tablennehas ◽  
Zoubir Dahmani ◽  
Meriem Mansouria Belhamiti ◽  
Amira Abdelnebi ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Caputo Derivative ◽  
Numerical Approach ◽  
Ulam Stability ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

AbstractIn this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane–Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivative, we investigate behaviors of the considered problem.

scholarly journals Convergence Analysis from the Solution of Riccati’s Fractional Differential Equation by Using Polynomial Least Squares Method

2020 ◽  
Vol 21 (1) ◽  
pp. 7-14
Author(s):  
Dian Nuryani ◽  
Endang Rusyaman ◽  
Betty Subartini
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Numerical Approach ◽  
Percentage Error ◽  
Mathematical Form ◽  
Fractional Differential

Riccati's Fractional Differential Equation (RFDE) has become a topic of study for researchers because RFDE can model variety of phenomenon in science such as random processes, optimal control and diffusion problems. Phenomena that can be modeled in a mathematical form can make it easier for humans to analyze several things from that phenomenon. RFDE generally does not have an exact solution, therefore a numerical approach solution is needed, one of the methods that gives good accuracy to the actual or exact solution is Polynomial Least Squares, where the errors calculated based on mean absolute percentage error (MAPE) produce a percentage below 1%. In addition, the convergence of a sequence from approximate solutions indicates that the sequence will converge to a solution.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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