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Journal Articles

Analysis and Fractal Dynamics of Local Fractional Partial Differential Equations Occurring in Physical Sciences

Ved Prakash Dubey, Jagdev Singh, Ahmed M. Alshehri, Sarvesh Dubey, Devendra Kumar

J. Comput. Nonlinear Dynam. March 2023, 18(3): 031001.

Paper No: CND-22-1153

DOI: https://doi.org/10.1115/1.4056360

Published Online: January 11, 2023

View Article titled, Analysis and Fractal Dynamics of Local Fractional Partial Differential Equations Occurring in Physical Sciences

Topics: Computer simulation, Fractals, Partial differential equations, Dynamics (Mechanics)

Journal Articles

Closure: to “Discussion on the Paper ‘Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller,’ Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16(12), p. 121002”

Kashif Ali Abro, Abdon Atangana

J. Comput. Nonlinear Dynam. February 2023, 18(2): 026001.

Paper No: CND-22-1241

DOI: https://doi.org/10.1115/1.4056399

Published Online: December 23, 2022

View Article titled, Closure: to “Discussion on the Paper ‘Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller,’ Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16(12), p. 121002”

Topics: Engines, Fractals, Motors, Rollers, Synchronization, Vibration equipment

Journal Articles

Fast and Stable Iterative Algorithm for Searching Wheel–Rail Contact Point Based on Geometry Constraint Equations

Jianbin Wang, Chunyuan Song, Dafu Zhang, Dadi Li, Sheng Qu

J. Comput. Nonlinear Dynam. January 2023, 18(1): 011004.

Paper No: CND-22-1164

DOI: https://doi.org/10.1115/1.4056134

Published Online: November 17, 2022

View Article titled, Fast and Stable Iterative Algorithm for Searching Wheel–Rail Contact Point Based on Geometry Constraint Equations

Topics: Constraint equations, Rails, Wheels, Geometry, B-splines, Algorithms, Fractals, Wheelsets

Journal Articles

Discussion on the Paper “Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller, Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16 (12), p. 121002”

Asterios Pantokratoras

J. Comput. Nonlinear Dynam. December 2022, 17(12): 125501.

Paper No: CND-22-1120

DOI: https://doi.org/10.1115/1.4055922

Published Online: October 25, 2022

View Article titled, Discussion on the Paper “Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller, Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16 (12), p. 121002”

Topics: Engines, Fractals, Motors, Rollers, Synchronization, Vibration equipment

Journal Articles

Computational Study of a Local Fractional Tricomi Equation Occurring in Fractal Transonic Flow

Sarvesh Dubey, Ved Prakash Dubey, Jagdev Singh, Ahmed M. Alshehri, Devendra Kumar

J. Comput. Nonlinear Dynam. August 2022, 17(8): 081006.

Paper No: CND-21-1261

DOI: https://doi.org/10.1115/1.4054482

Published Online: June 7, 2022

View Article titled, Computational Study of a Local Fractional Tricomi Equation Occurring in Fractal Transonic Flow

Topics: Computer simulation, Fractals, Transonic flow, Approximation

Journal Articles

On Solutions of the Stiff Differential Equations in Chemistry Kinetics With Fractal-Fractional Derivatives

Muhammad Farman, Muhammad Aslam, Ali Akgül, Fahd Jarad

J. Comput. Nonlinear Dynam. July 2022, 17(7): 071007.

Paper No: CND-21-1148

DOI: https://doi.org/10.1115/1.4054347

Published Online: May 18, 2022

View Article titled, On Solutions of the Stiff Differential Equations in Chemistry Kinetics With Fractal-Fractional Derivatives

Topics: Chemistry, Differential equations, Fractals

Journal Articles

From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrödinger and Classical Wave Equation

Luis Vázquez, M. Pilar Velasco, Dumitru Baleanu, J. Luis Vázquez-Poletti, Salvador Jiménez

J. Comput. Nonlinear Dynam. August 2022, 17(8): 080801.

Paper No: CND-21-1355

DOI: https://doi.org/10.1115/1.4054153

Published Online: April 1, 2022

View Article titled, From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrödinger and Classical Wave Equation

Topics: Approximation, Schrödinger equation, Wave equations, Fractals, Maxwell equations, Cloud computing, Electromagnetic wave propagation, Wavelength

Journal Articles

Early Wear Fault Dynamics Analysis Method of Gear Coupled Rotor System Based on Dynamic Fractal Backlash

Wujiu Pan, Liangyu Ling, Haoyong Qu, Minghai Wang

J. Comput. Nonlinear Dynam. January 2022, 17(1): 011003.

Paper No: CND-21-1037

DOI: https://doi.org/10.1115/1.4052650

Published Online: November 5, 2021

View Article titled, Early Wear Fault Dynamics Analysis Method of Gear Coupled Rotor System Based on Dynamic Fractal Backlash

Topics: Fractals, Gears, Rotors, Wear

Journal Articles

Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller

Kashif Ali Abro, Abdon Atangana

J. Comput. Nonlinear Dynam. December 2021, 16(12): 121002.

Paper No: CND-21-1062

DOI: https://doi.org/10.1115/1.4052189

Published Online: September 22, 2021

View Article titled, Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller

Topics: Fractals, Motors, Rollers, Rolling mills, Vibration equipment

Journal Articles

The Influence of Tooth Surface Wear on Dynamic Characteristics of Gear-Bearing System Based on Fractal Theory

Xiaopeng Li, Jinchi Xu, Zemin Yang, Renzhen Chen, Hexu Yang

J. Comput. Nonlinear Dynam. April 2020, 15(4): 041004.

Paper No: CND-19-1342

DOI: https://doi.org/10.1115/1.4046053

Published Online: February 24, 2020

View Article titled, The Influence of Tooth Surface Wear on Dynamic Characteristics of Gear-Bearing System Based on Fractal Theory

Topics: Bearings, Fractals, Gears, Wear, Stiffness, Friction

Journal Articles

A Detailed Look at the SLIP Model Dynamics: Bifurcations, Chaotic Behavior, and Fractal Basins of Attraction

Petr Zaytsev, Tom Cnops, C. David Remy

J. Comput. Nonlinear Dynam. August 2019, 14(8): 081002.

Paper No: CND-18-1416

DOI: https://doi.org/10.1115/1.4043453

Published Online: May 13, 2019

View Article titled, A Detailed Look at the SLIP Model Dynamics: Bifurcations, Chaotic Behavior, and Fractal Basins of Attraction

Topics: Bifurcation, Dynamics (Mechanics), Energy levels (Quantum mechanics), Flight, Fractals, Pendulums, Robots, Springs, Poincaré maps, Stability

Journal Articles

Energy Straggling Function by F α -Calculus

Saleh Ashrafi, Ali Khalili Golmankhaneh

J. Comput. Nonlinear Dynam. September 2017, 12(5): 051010.

Paper No: CND-16-1304

DOI: https://doi.org/10.1115/1.4035718

Published Online: May 4, 2017

View Article titled, Energy Straggling Function by F α -Calculus

Topics: Fractals, Particulate matter

Journal Articles

Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects

Kambiz Razminia, Abolhassan Razminia, J. A. Tenreiro Machado

J. Comput. Nonlinear Dynam. January 2016, 11(1): 011006.

Paper No: CND-14-1160

DOI: https://doi.org/10.1115/1.4030534

Published Online: January 1, 2016

View Article titled, Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects

Topics: Flow (Dynamics), Fractals, Pressure, Reservoirs, Skin, Storage

Journal Articles

Gear Dynamics Analysis With Turbulent Journal Bearings Under Quadratic Damping and Nonlinear Suspension—Bifurcation and Chaos

Cai-Wan Chang-Jian

J. Comput. Nonlinear Dynam. January 2013, 8(1): 011013.

Paper No: CND-11-1067

DOI: https://doi.org/10.1115/1.4006203

Published Online: June 22, 2012

View Article titled, Gear Dynamics Analysis With Turbulent Journal Bearings Under Quadratic Damping and Nonlinear Suspension—Bifurcation and Chaos

Topics: Bearings, Bifurcation, Damping, Gears, Turbulence, Fractals, Dynamics (Mechanics), Dimensions, Chaos, Poincaré maps

Journal Articles

A Nonlinear Noise Reduction Approach to Vibration Analysis for Bearing Health Diagnosis

Ruqiang Yan, Robert X. Gao

J. Comput. Nonlinear Dynam. April 2012, 7(2): 021004.

DOI: https://doi.org/10.1115/1.4005463

Published Online: January 6, 2012

View Article titled, A Nonlinear Noise Reduction Approach to Vibration Analysis for Bearing Health Diagnosis

Topics: Bearings, Noise (Sound), Noise control, Phase space, Signals, Vibration, Time series, Fractals, Algorithms, Rolling bearings

Journal Articles

Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model

Diego Orlando, Paulo B. Gonçalves, Giuseppe Rega, Stefano Lenci

J. Comput. Nonlinear Dynam. October 2011, 6(4): 041014.

DOI: https://doi.org/10.1115/1.4003880

Published Online: June 14, 2011

View Article titled, Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model

Topics: Bifurcation, Buckling, Erosion, Stability, Stress, Nonlinear dynamics, Fractals, Safety, Potential energy

Journal Articles

Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

Robert A. Van Gorder, S. Roy Choudhury

J. Comput. Nonlinear Dynam. April 2011, 6(2): 021013.

DOI: https://doi.org/10.1115/1.4002685

Published Online: November 15, 2010

View Article titled, Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

Topics: Chaos, Equilibrium (Physics), Homoclinic orbits, Stability, Theorems (Mathematics), Dynamic systems, Fractals, Nonlinear systems

Journal Articles

Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

Meng Xu, Ziyou Gao

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021206.

DOI: https://doi.org/10.1115/1.2833905

Published Online: February 4, 2008

View Article titled, Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

Topics: Dimensions, Flow (Dynamics), Traffic, Fractals, Chaos, Density, Dynamic systems

Journal citation

NARROW

Analysis and Fractal Dynamics of Local Fractional Partial Differential Equations Occurring in Physical Sciences

Closure: to “Discussion on the Paper ‘Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller,’ Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16(12), p. 121002”

Fast and Stable Iterative Algorithm for Searching Wheel–Rail Contact Point Based on Geometry Constraint Equations

Discussion on the Paper “Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller, Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16 (12), p. 121002”

Computational Study of a Local Fractional Tricomi Equation Occurring in Fractal Transonic Flow

On Solutions of the Stiff Differential Equations in Chemistry Kinetics With Fractal-Fractional Derivatives

From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrödinger and Classical Wave Equation

Early Wear Fault Dynamics Analysis Method of Gear Coupled Rotor System Based on Dynamic Fractal Backlash

Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller

The Influence of Tooth Surface Wear on Dynamic Characteristics of Gear-Bearing System Based on Fractal Theory

A Detailed Look at the SLIP Model Dynamics: Bifurcations, Chaotic Behavior, and Fractal Basins of Attraction

Energy Straggling Function by F α -Calculus

Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects

Gear Dynamics Analysis With Turbulent Journal Bearings Under Quadratic Damping and Nonlinear Suspension—Bifurcation and Chaos

A Nonlinear Noise Reduction Approach to Vibration Analysis for Bearing Health Diagnosis

Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model

Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

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