Results 11 to 20 of about 9,271,467 (193)

Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series

Symmetry, 2022
This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination of the Laplace transformation and the residual power series technique, we achieve analytic and approximation results in rapid ...
Kamsing Nonlaopon, Shaban Aly, Naveed Iqbal   +2 more
exaly   +4 more sources

Laplace Residual Power Series Method for Solving Three-Dimensional Fractional Helmholtz Equations

Symmetry, 2023
In the present study, the exact solutions of the fractional three-dimensional (3D) Helmholtz equation (FHE) are obtained using the Laplace residual power series method (LRPSM). The fractional derivative is calculated using the Caputo operator. First, we introduce a novel method that combines the Laplace transform tool and the residual power series ...
Samir El-Tantawy, Kamsing Nonlaopon, Rasool Shah   +2 more
exaly   +3 more sources

Constructing Analytical Solutions of the Fractional Riccati Differential Equations Using Laplace Residual Power Series Method

Fractal and Fractional, 2022
In this article, a hybrid numerical technique combining the Laplace transform and residual power series method is used to construct a series solution of the nonlinear fractional Riccati differential equation in the sense of Caputo fractional derivative ...
Aliaa Burqan, Aref Sarhan, Rania Saadeh
doaj   +3 more sources

Solving Nonlinear Fractional PDEs with Applications to Physics and Engineering Using the Laplace Residual Power Series Method

International Journal of Differential Equations, 2023
The Laplace residual power series (LRPS) method uses the Caputo fractional derivative definition to solve nonlinear fractional partial differential equations. This technique has been applied successfully to solve equations such as the fractional Kuramoto–
Khalid K. Ali, F. E. Abd Elbary, Mohamed S. Abdel-Wahed, M. A. Elsisy, Mourad S. Semary   +4 more
doaj   +3 more sources

Comparative Analysis of the Time-Fractional Black–Scholes Option Pricing Equations (BSOPE) by the Laplace Residual Power Series Method (LRPSM)

Journal of Mathematics, 2023
The residual power series method is effective for obtaining solutions to fractional-order differential equations. However, the procedure needs the n−1ϖ derivative of the residual function.
Muhammad Imran Liaqat, Eric Okyere
doaj   +3 more sources

On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method

Fractal and Fractional
In this work, we first develop the modified time Caputo fractional Kawahara Equations (MTCFKEs) in the usual Hilbert spaces and extend them to analogous structures within the theory of Hilbert algebras.
Faten H. Damag, Amin Saif
doaj   +3 more sources

Modeling and analysis of dengue transmission in fuzzy-fractional framework: a hybrid residual power series approach [PDF]

Scientific Reports
The current manuscript presents a mathematical model of dengue fever transmission with an asymptomatic compartment to capture infection dynamics in the presence of uncertainty. The model is fuzzified using triangular fuzzy numbers (TFNs) approach.
Mubashir Qayyum, Qursam Fatima, Ali Akgül, Murad Khan Hassani   +3 more
doaj   +3 more sources

Numerical solution of two-dimensional fractional differential equations using Laplace transform with residual power series method

Nonlinear Engineering
One of the efficient and reliable methods for resolving fractional order linear as well as non-linear differential equations is the Laplace transform with residual power series method. This approach is used in the current research to obtain the numerical
Pant Rajendra, Arora Geeta, Singh Brajesh Kumar, Emadifar Homan   +3 more
doaj   +3 more sources

Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method

Mathematics, 2022
Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand the complexity of these phenomena.
Hussam Aljarrah, Mohammad Alaroud, Anuar Ishak, Maslina Darus   +3 more
doaj   +2 more sources

A Laplace-Embedded Residual Power Series Framework

Gulf Journal of Mathematics
This paper presents a hybrid analytical approach, combining the residual power series method with the Laplace transform, to solve systems of linear and nonlinear differential equations. The proposed technique converts governing differential systems into algebraic representations, naturally incorporating initial conditions without numerical ...
Hana Mokeddem, Mountassir Hamdi Cherif, Bachir Djebbar, Djelloul Ziane   +3 more
openaire   +2 more sources