Employing the Laplace Residual Power Series Method to Solve (1+1)- and (2+1)-Dimensional Time-Fractional Nonlinear Differential Equations
In this paper, we present a highly efficient analytical method that combines the Laplace transform and the residual power series approach to approximate solutions of nonlinear time-fractional partial differential equations (PDEs). First, we derive the analytical method for a general form of fraction...
| Published in: | Fractal and Fractional |
|---|---|
| Main Authors: | Adel R. Hadhoud, Abdulqawi A. M. Rageh, Taha Radwan |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-07-01
|
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/7/401 |
Similar Items
Exact and Approximate Solutions for Linear and Nonlinear Partial Differential Equations via Laplace Residual Power Series Method
by: Haneen Khresat, et al.
Published: (2023-07-01)
by: Haneen Khresat, et al.
Published: (2023-07-01)
Constructing Analytical Solutions of the Fractional Riccati Differential Equations Using Laplace Residual Power Series Method
by: Aliaa Burqan, et al.
Published: (2022-12-01)
by: Aliaa Burqan, et al.
Published: (2022-12-01)
A comparative analysis using the Laplace transform approach for some nonlinear fractional physical problems
by: Mohammad Alaroud
Published: (2025-09-01)
by: Mohammad Alaroud
Published: (2025-09-01)
On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method
by: Faten H. Damag, et al.
Published: (2025-05-01)
by: Faten H. Damag, et al.
Published: (2025-05-01)
Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations
by: M. Mossa Al-Sawalha, et al.
Published: (2023-01-01)
by: M. Mossa Al-Sawalha, et al.
Published: (2023-01-01)
Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System
by: Mohammed Shqair, et al.
Published: (2023-02-01)
by: Mohammed Shqair, et al.
Published: (2023-02-01)
Numerical solution of two-dimensional fractional differential equations using Laplace transform with residual power series method
by: Pant Rajendra, et al.
Published: (2024-03-01)
by: Pant Rajendra, et al.
Published: (2024-03-01)
Efficient Solution of Fractional System Partial Differential Equations Using Laplace Residual Power Series Method
by: Ahmad Shafee, et al.
Published: (2023-05-01)
by: Ahmad Shafee, et al.
Published: (2023-05-01)
A Novel Analytical LRPSM for Solving Nonlinear Systems of FPDEs
by: Hussam Aljarrah, et al.
Published: (2022-11-01)
by: Hussam Aljarrah, et al.
Published: (2022-11-01)
On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations
by: Rawya Al-deiakeh, et al.
Published: (2025-04-01)
by: Rawya Al-deiakeh, et al.
Published: (2025-04-01)
Application of the generalized integral Laplace transform to solving differential equations
by: Svetlana M Zaikina
Published: (2011-12-01)
by: Svetlana M Zaikina
Published: (2011-12-01)
A Reliable Technique for Solving Fractional Partial Differential Equation
by: Azzh Saad Alshehry, et al.
Published: (2022-10-01)
by: Azzh Saad Alshehry, et al.
Published: (2022-10-01)
Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method
by: Hussam Aljarrah, et al.
Published: (2022-06-01)
by: Hussam Aljarrah, et al.
Published: (2022-06-01)
Extracting explicit coefficient formulas: A robust approach to the laplace residual power series method
by: Pisamai Kittipoom
Published: (2024-12-01)
by: Pisamai Kittipoom
Published: (2024-12-01)
Laplace transform of fractional order differential equations
by: Song Liang, et al.
Published: (2015-05-01)
by: Song Liang, et al.
Published: (2015-05-01)
A New Higher-Order Convergence Laplace–Fourier Method for Linear Neutral Delay Differential Equations
by: Gilbert Kerr, et al.
Published: (2025-03-01)
by: Gilbert Kerr, et al.
Published: (2025-03-01)
Solving System of a Linear Fractional Differential Equations by Using Laplace Transformation
by: Shaker Rashid, et al.
Published: (2007-12-01)
by: Shaker Rashid, et al.
Published: (2007-12-01)
A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework
by: Azzh Saad Alshehry
Published: (2023-12-01)
by: Azzh Saad Alshehry
Published: (2023-12-01)
Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation
by: M. Mossa Al-Sawalha, et al.
Published: (2025-03-01)
by: M. Mossa Al-Sawalha, et al.
Published: (2025-03-01)
Applications of Fractional-Laplace Transformation in the Field of Electrical Engineering
by: Ali Moazzam, et al.
Published: (2023-08-01)
by: Ali Moazzam, et al.
Published: (2023-08-01)
On solutions of fractional differential equations for the mechanical oscillations by using the Laplace transform
by: Changdev P. Jadhav, et al.
Published: (2024-11-01)
by: Changdev P. Jadhav, et al.
Published: (2024-11-01)
An integrated Laplace transform and accelerated Adomian decomposition approach for solving time-fractional nonlinear partial differential equations
by: Mohamed A. Ramadan, et al.
Published: (2025-08-01)
by: Mohamed A. Ramadan, et al.
Published: (2025-08-01)
Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique
by: Aref Sarhan, et al.
Published: (2022-10-01)
by: Aref Sarhan, et al.
Published: (2022-10-01)
Some applications of Laplace transforms in models with impulses or discontinuous forcing functions
by: Diego Miranda Gonçalves, et al.
Published: (2024-01-01)
by: Diego Miranda Gonçalves, et al.
Published: (2024-01-01)
Laplace Adomian decomposition method for solving a fish farm model
by: Sambath M., et al.
Published: (2016-09-01)
by: Sambath M., et al.
Published: (2016-09-01)
Promoted residual power series technique with Laplace transform to solve some time-fractional problems arising in physics
by: Marwan Alquran, et al.
Published: (2020-12-01)
by: Marwan Alquran, et al.
Published: (2020-12-01)
Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method
by: J. Prakash, et al.
Published: (2016-03-01)
by: J. Prakash, et al.
Published: (2016-03-01)
The Double Laplace–Adomian Method for Solving Certain Nonlinear Problems in Applied Mathematics
by: Oswaldo González-Gaxiola
Published: (2025-08-01)
by: Oswaldo González-Gaxiola
Published: (2025-08-01)
A comparative study on residual power series method and differential transform method through the time-fractional telegraph equation
by: Devshali Pratiksha, et al.
Published: (2025-04-01)
by: Devshali Pratiksha, et al.
Published: (2025-04-01)
The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature
by: Abdur Rab, et al.
Published: (2024-04-01)
by: Abdur Rab, et al.
Published: (2024-04-01)
Analyzing the fractional order T. Regge problem using the Laplace transformation method
by: Hozan Hilmi, et al.
Published: (2024-12-01)
by: Hozan Hilmi, et al.
Published: (2024-12-01)
Applications of the Laplace variational iteration method to fractional heat like equations
by: Alok Bhargava, et al.
Published: (2023-12-01)
by: Alok Bhargava, et al.
Published: (2023-12-01)
EXTENSION OF LAPLACE – ARA TRANSFORM OF DIFFERENTIAL EQUATIONS
by: Dilip Kumar Jaiswal, et al.
Published: (2024-10-01)
by: Dilip Kumar Jaiswal, et al.
Published: (2024-10-01)
Comparison of the results obtained by Iman transform with Laplace transform
by: NIHAL OZDOGAN
Published: (2024-12-01)
by: NIHAL OZDOGAN
Published: (2024-12-01)
Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method
by: Michelle Sherman, et al.
Published: (2022-09-01)
by: Michelle Sherman, et al.
Published: (2022-09-01)
Analytic technique for solving temporal time-fractional gas dynamics equations with Caputo fractional derivative
by: Mohammad Alaroud, et al.
Published: (2022-08-01)
by: Mohammad Alaroud, et al.
Published: (2022-08-01)
Generalization of fractional Laplace transform for higher order and its application
by: Ahmed Bouchenak
Published: (2021-12-01)
by: Ahmed Bouchenak
Published: (2021-12-01)
Laplace Adomian decomposition method for integro differential equations on time scale
by: Shafiq Hussain, et al.
Published: (2025-02-01)
by: Shafiq Hussain, et al.
Published: (2025-02-01)
Fractional analysis of non-linear fuzzy partial differential equations by using a direct procedure
by: Muhammad Arshad, et al.
Published: (2024-04-01)
by: Muhammad Arshad, et al.
Published: (2024-04-01)
Implementation of Yang residual power series method to solve fractional non-linear systems
by: Azzh Saad Alshehry, et al.
Published: (2023-02-01)
by: Azzh Saad Alshehry, et al.
Published: (2023-02-01)
Similar Items
-
Exact and Approximate Solutions for Linear and Nonlinear Partial Differential Equations via Laplace Residual Power Series Method
by: Haneen Khresat, et al.
Published: (2023-07-01) -
Constructing Analytical Solutions of the Fractional Riccati Differential Equations Using Laplace Residual Power Series Method
by: Aliaa Burqan, et al.
Published: (2022-12-01) -
A comparative analysis using the Laplace transform approach for some nonlinear fractional physical problems
by: Mohammad Alaroud
Published: (2025-09-01) -
On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method
by: Faten H. Damag, et al.
Published: (2025-05-01) -
Combination of Laplace transform and residual power series techniques of special fractional-order non-linear partial differential equations
by: M. Mossa Al-Sawalha, et al.
Published: (2023-01-01)
