Results 1 to 10 of about 9,271,467 (193)

Laplace-Residual Power Series Method for Solving Time-Fractional Reaction–Diffusion Model

Fractal and Fractional, 2023
Despite the fact the Laplace transform has an appreciable efficiency in solving many equations, it cannot be employed to nonlinear equations of any type.
Moa’ath N. Oqielat, Tareq Eriqat, Osama Ogilat, Ahmad El-Ajou, Sharifah E. Alhazmi, Shrideh Al-Omari   +5 more
doaj   +5 more sources

Efficient Solution of Fractional System Partial Differential Equations Using Laplace Residual Power Series Method

Fractal and Fractional, 2023
In this paper, we present an efficient solution method for solving fractional system partial differential equations (FSPDEs) using the Laplace residual power series (LRPS) method.
Ahmad Shafee, Yousuf Alkhezi, Rasool Shah   +2 more
doaj   +5 more sources

Exact and Approximate Solutions for Linear and Nonlinear Partial Differential Equations via Laplace Residual Power Series Method

Axioms, 2023
The Laplace residual power series method was introduced as an effective technique for finding exact and approximate series solutions to various kinds of differential equations.
Haneen Khresat, Ahmad El-Ajou, Shrideh Al-Omari, Sharifah E. Alhazmi, Moa’ath N. Oqielat   +4 more
doaj   +5 more sources

Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System

Fractal and Fractional, 2023
In this paper, a system of coupled fractional neutron diffusion equations with delayed neutrons was solved efficiently by using a combination of residual power series and Laplace transform techniques, and the anomalous diffusion was considered by taking ...
Mohammed Shqair, Ibrahim Ghabar, Aliaa Burqan   +2 more
doaj   +5 more sources

General Residual Power Series Method: Explicit Coefficient Derivation and Unified Laplace-like Transform Approach for Fractional PDEs

Mathematics
This work introduces the General Residual Power Series Method (GRPSM) as a unified analytical framework encompassing the conventional Residual Power Series Method (RPSM) and its Laplace-like transform variants. By deriving a universal coefficient formula,
Pisamai Kittipoom, Jessada Tanthanuch
doaj   +5 more sources

Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique

Fractal and Fractional, 2022
In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations (T-FCB-BEs) using Laplace-residual power series (L-RPS) technique in the sense of Caputo fractional derivative (C-FD).
Aref Sarhan, Aliaa Burqan, Rania Saadeh, Zeyad Al-Zhour   +3 more
doaj   +5 more sources

Application of Laplace residual power series method for approximate solutions of fractional IVP’s

Alexandria Engineering Journal, 2022
In this study, different systems of linear and non-linear fractional initial value problems are solved analytically utilizing an attractive novel technique so-called the Laplace residual power series approach, and which is based on the coupling of the ...
Mohammad Alaroud
doaj   +4 more sources

Adapting Laplace residual power series approach to the Caudrey Dodd Gibbon equation [PDF]

Scientific Reports
In real-life applications, nonlinear differential equations play an essential role in representing many phenomena. One well-known nonlinear differential equation that helps describe and explain many chemicals, physical, and biological processes is the ...
Samy A. Abdelhafeez, Anas A. M. Arafa, Yousef H. Zahran, Ibrahim S. I. Osman, Moutaz Ramadan   +4 more
doaj   +4 more sources

Combination of Laplace transform and residual power series techniques to solve autonomous n-dimensional fractional nonlinear systems [PDF]

Nonlinear Engineering, 2021
In this work, a new iterative algorithm is presented to solve autonomous n-dimensional fractional nonlinear systems analytically. The suggested scheme is combination of two methods; the Laplace transform and the residual power series.
Alquran Marwan, Alsukhour Maysa, Ali Mohammed, Jaradat Imad   +3 more
doaj   +3 more sources

Extracting explicit coefficient formulas: A robust approach to the laplace residual power series method

Alexandria Engineering Journal
This work presents a novel advancement to the Laplace Residual Power Series Method (LRPSM) for solving fractional differential equations by specifically utilizing the Caputo fractional derivative.
Pisamai Kittipoom
doaj   +4 more sources