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Journal Articles

A New Perspective for Scientific Modelling: Sparse Reconstruction-Based Approach for Learning Time-Space Fractional Differential Equations

Yash Vats, Mani Mehra, Dietmar Oelz, Abhishek Kumar Singh

Publisher: ASME

J. Comput. Nonlinear Dynam. December 2024, 19(12): 121003.

Paper No: CND-24-1099

https://doi.org/10.1115/1.4066330

Published Online: September 21, 2024

View Article titled, A New Perspective for Scientific Modelling: Sparse Reconstruction-Based Approach for Learning Time-Space Fractional Differential Equations

Topics: Differential equations, Diffusion (Physics), Noise (Sound), Algorithms, Wave equations, Modeling

Journal Articles

High-Order Approximation to Caputo Derivative on Graded Mesh and Time-Fractional Diffusion Equation for Nonsmooth Solutions

Shweta Kumari, Abhishek Kumar Singh, Vaibhav Mehandiratta, Mani Mehra

Publisher: ASME

J. Comput. Nonlinear Dynam. October 2024, 19(10): 101001.

Paper No: CND-23-1297

https://doi.org/10.1115/1.4066023

Published Online: August 20, 2024

View Article titled, High-Order Approximation to Caputo Derivative on Graded Mesh and Time-Fractional Diffusion Equation for Nonsmooth Solutions

Topics: Approximation, Diffusion (Physics), Errors, Stability, Interpolation

Journal Articles

Full-Dimensional Proportional-Derivative Control Technique for Turing Pattern and Bifurcation of Delayed Reaction-Diffusion Bidirectional Ring Neural Networks

Xiangyu Du, Min Xiao, Yifeng Luan, Jie Ding, Leszek Rutkowski

Publisher: ASME

J. Comput. Nonlinear Dynam. September 2024, 19(9): 091002.

Paper No: CND-23-1224

https://doi.org/10.1115/1.4065881

Published Online: July 13, 2024

View Article titled, Full-Dimensional Proportional-Derivative Control Technique for Turing Pattern and Bifurcation of Delayed Reaction-Diffusion Bidirectional Ring Neural Networks

Topics: Artificial neural networks, Bifurcation, Control equipment, Delays, Diffusion (Physics), Stability

Journal Articles

Analytical Properties and Numerical Preservation of an Age-Group Susceptible-Infected-Recovered Model: Application to the Diffusion of Information

Angelamaria Cardone, Patricia Diaz de Alba, Beatrice Paternoster

Publisher: ASME

J. Comput. Nonlinear Dynam. June 2024, 19(6): 061006.

Paper No: CND-23-1152

https://doi.org/10.1115/1.4065437

Published Online: May 21, 2024

View Article titled, Analytical Properties and Numerical Preservation of an Age-Group Susceptible-Infected-Recovered Model: Application to the Diffusion of Information

Topics: Diffusion (Physics), Finite difference methods, Preservation, Approximation

Journal Articles

α-Robust Error Analysis of L2- 1 σ Scheme on Graded Mesh for Time-Fractional Nonlocal Diffusion Equation

Pari J. Kundaliya

Publisher: ASME

J. Comput. Nonlinear Dynam. May 2024, 19(5): 051004.

Paper No: CND-23-1173

https://doi.org/10.1115/1.4065011

Published Online: March 21, 2024

View Article titled, α-Robust Error Analysis of L2- 1 σ Scheme on Graded Mesh for Time-Fractional Nonlocal Diffusion Equation

Topics: Diffusion (Physics), Errors, Error analysis, Theorems (Mathematics)

Journal Articles

Solutions of Time-Space Fractional Partial Differential Equations Using Picard's Iterative Method

Manoj Kumar, Aman Jhinga, J. T. Majithia

Publisher: ASME

J. Comput. Nonlinear Dynam. March 2024, 19(3): 031006.

Paper No: CND-23-1185

https://doi.org/10.1115/1.4064553

Published Online: February 7, 2024

View Article titled, Solutions of Time-Space Fractional Partial Differential Equations Using Picard's Iterative Method

Topics: Diffusion (Physics), Iterative methods, Partial differential equations, Thin films, Convection, Heat

Journal Articles

On the Inverse Problem of Time-Dependent Coefficient in a Time Fractional Diffusion Problem by Newly Defined Monic Laquerre Wavelets

Mine A. Bayrak, Ali Demir

Publisher: ASME

J. Comput. Nonlinear Dynam. November 2023, 18(11): 111003.

Paper No: CND-23-1089

https://doi.org/10.1115/1.4063337

Published Online: September 14, 2023

View Article titled, On the Inverse Problem of Time-Dependent Coefficient in a Time Fractional Diffusion Problem by Newly Defined Monic Laquerre Wavelets

Topics: Diffusion (Physics), Inverse problems, Wavelets, Polynomials, Algorithms

Journal Articles

Exact Solutions of Systems of Nonlinear Time-Space Fractional Partial Differential Equations Using an Iterative Method

Manoj Kumar

Publisher: ASME

J. Comput. Nonlinear Dynam. October 2023, 18(10): 101003.

Paper No: CND-22-1295

https://doi.org/10.1115/1.4062910

Published Online: July 26, 2023

View Article titled, Exact Solutions of Systems of Nonlinear Time-Space Fractional Partial Differential Equations Using an Iterative Method

Topics: Diffusion (Physics), Partial differential equations, Error analysis, Iterative methods

Journal Articles

On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel

Anh Tuan Nguyen, Van Tien Nguyen, Dumitru Baleanu, Van Thinh Nguyen

Publisher: ASME

J. Comput. Nonlinear Dynam. May 2023, 18(5): 051006.

Paper No: CND-22-1113

https://doi.org/10.1115/1.4062198

Published Online: April 5, 2023

View Article titled, On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel

Topics: Diffusion (Physics), Space, Dimensions, Theorems (Mathematics)

Journal Articles

Numerical Solution for a Nonlinear Time-Space Fractional Convection-Diffusion Equation

Merfat Basha, Eyaya Fekadie Anley, Binxiang Dai

Publisher: ASME

J. Comput. Nonlinear Dynam. January 2023, 18(1): 011006.

Paper No: CND-21-1250

https://doi.org/10.1115/1.4056218

Published Online: November 21, 2022

View Article titled, Numerical Solution for a Nonlinear Time-Space Fractional Convection-Diffusion Equation

Topics: Convection, Diffusion (Physics), Nonlinear systems, Stability, Errors, Approximation

Journal Articles

A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates

Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh

Publisher: ASME

J. Comput. Nonlinear Dynam. July 2022, 17(7): 071008.

Paper No: CND-21-1353

https://doi.org/10.1115/1.4054483

Published Online: May 24, 2022

View Article titled, A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates

Topics: Chemical reactions, Errors, Flow (Dynamics), Mixed convection, Partial differential equations, Plates (structures), Stability, Diffusion (Physics), Convection, Scalars

Journal Articles

Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation

Kushal Dhar Dwivedi, Rajeev, Subir Das, Dumitru Baleanu

Publisher: ASME

J. Comput. Nonlinear Dynam. June 2020, 15(6): 061005.

Paper No: CND-19-1288

https://doi.org/10.1115/1.4046879

Published Online: April 27, 2020

View Article titled, Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation

Topics: Diffusion (Physics), Polynomials, Spacetime, Error analysis, Boundary-value problems, Approximation, Numerical analysis

Journal Articles

Multistability and Stochastic Phenomena in the Distributed Brusselator Model

Alexander Kolinichenko, Lev Ryashko

Publisher: ASME

J. Comput. Nonlinear Dynam. January 2020, 15(1): 011007.

Paper No: CND-19-1096

https://doi.org/10.1115/1.4045405

Published Online: November 22, 2019

View Article titled, Multistability and Stochastic Phenomena in the Distributed Brusselator Model

Topics: Attractors, Bifurcation, Noise (Sound), Pattern formation, Transients (Dynamics), Oscillations, Diffusion (Physics), Computer simulation

Journal Articles

New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

Feras Yousef, Marwan Alquran, Imad Jaradat, Shaher Momani, Dumitru Baleanu

Publisher: ASME

J. Comput. Nonlinear Dynam. November 2019, 14(11): 111008.

Paper No: CND-19-1086

https://doi.org/10.1115/1.4044585

Published Online: September 23, 2019

View Article titled, New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

Topics: Diffusion (Physics), Partial differential equations

Journal Articles

A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation

Yong Xu, Qixian Liu, Jike Liu, Yanmao Chen

Publisher: ASME

J. Comput. Nonlinear Dynam. August 2019, 14(8): 081005.

Paper No: CND-19-1008

https://doi.org/10.1115/1.4043525

Published Online: May 13, 2019

View Article titled, A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation

Topics: Boundary-value problems, Differential equations, Separation (Technology), Algorithms, Diffusion (Physics)

Journal Articles

Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations

Masataka Fukunaga

Publisher: ASME

J. Comput. Nonlinear Dynam. June 2019, 14(6): 061005.

Paper No: CND-18-1453

https://doi.org/10.1115/1.4043149

Published Online: April 8, 2019

View Article titled, Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations

Topics: Diffusion (Physics), Oscillations, Algorithms

Journal Articles

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

Anup Singh, S. Das, S. H. Ong, H. Jafari

Publisher: ASME

J. Comput. Nonlinear Dynam. April 2019, 14(4): 041003.

Paper No: CND-18-1173

https://doi.org/10.1115/1.4042687

Published Online: February 15, 2019

View Article titled, Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

Topics: Approximation, Diffusion (Physics), Stability, Boundary-value problems

Journal Articles

Complex Wave Solutions to Mathematical Biology Models I: Newell–Whitehead–Segel and Zeldovich Equations

Alper Korkmaz

Publisher: ASME

J. Comput. Nonlinear Dynam. August 2018, 13(8): 081004.

Paper No: CND-18-1042

https://doi.org/10.1115/1.4040411

Published Online: June 18, 2018

View Article titled, Complex Wave Solutions to Mathematical Biology Models I: Newell–Whitehead–Segel and Zeldovich Equations

Topics: Biology, Traveling waves, Waves, Diffusion (Physics), Dynamics (Mechanics), Nonlinear dynamical systems

Journal Articles

Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

Ivanka M. Stamova, Stanislav Simeonov

Publisher: ASME

J. Comput. Nonlinear Dynam. January 2018, 13(1): 011015.

Paper No: CND-17-1274

https://doi.org/10.1115/1.4038290

Published Online: November 17, 2017

View Article titled, Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

Topics: Artificial neural networks, Diffusion (Physics), Stability, Synchronization, Equilibrium (Physics)

Journal Articles

The Transport Dynamics Induced by Riesz Potential in Modeling Fractional Reaction–Diffusion-Mechanics System

S. Saha Ray

Publisher: ASME

J. Comput. Nonlinear Dynam. February 2018, 13(2): 021005.

Paper No: CND-17-1223

https://doi.org/10.1115/1.4037418

Published Online: November 1, 2017

View Article titled, The Transport Dynamics Induced by Riesz Potential in Modeling Fractional Reaction–Diffusion-Mechanics System

Topics: Diffusion (Physics), Approximation, Modeling, Dynamics (Mechanics)

Journal citation

NARROW

A New Perspective for Scientific Modelling: Sparse Reconstruction-Based Approach for Learning Time-Space Fractional Differential Equations

High-Order Approximation to Caputo Derivative on Graded Mesh and Time-Fractional Diffusion Equation for Nonsmooth Solutions

Full-Dimensional Proportional-Derivative Control Technique for Turing Pattern and Bifurcation of Delayed Reaction-Diffusion Bidirectional Ring Neural Networks

Analytical Properties and Numerical Preservation of an Age-Group Susceptible-Infected-Recovered Model: Application to the Diffusion of Information

α-Robust Error Analysis of L2- 1 σ Scheme on Graded Mesh for Time-Fractional Nonlocal Diffusion Equation

Solutions of Time-Space Fractional Partial Differential Equations Using Picard's Iterative Method

On the Inverse Problem of Time-Dependent Coefficient in a Time Fractional Diffusion Problem by Newly Defined Monic Laquerre Wavelets

Exact Solutions of Systems of Nonlinear Time-Space Fractional Partial Differential Equations Using an Iterative Method

On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel

Numerical Solution for a Nonlinear Time-Space Fractional Convection-Diffusion Equation

A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates

Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation

Multistability and Stochastic Phenomena in the Distributed Brusselator Model

New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation

Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

Complex Wave Solutions to Mathematical Biology Models I: Newell–Whitehead–Segel and Zeldovich Equations

Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

The Transport Dynamics Induced by Riesz Potential in Modeling Fractional Reaction–Diffusion-Mechanics System

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