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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

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   +2 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   +2 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   +2 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

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   +2 more sources

Fractional analysis of non-linear fuzzy partial differential equations by using a direct procedure [PDF]

Scientific Reports
In this study, an accurate analytical solution is presented for fuzzy FPDEs. It is done by using a novel method called the Laplace-residual power series (LRPSM) to build a series solution to the given problems. The fundamental instruments of the employed
Muhammad Arshad, Shahbaz Khan, Hassan Khan, Hamid Ali, Ijaz Ali   +4 more
doaj   +2 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   +2 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   +2 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   +2 more sources