Results 11 to 20 of about 39,417 (134)

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

Fractal and Fractional, 2023
In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics.
Zainab Alsheekhhussain, Khaled Moaddy, Rasool Shah, Saleh Alshammari, Mohammad Alshammari, M. Mossa Al-Sawalha, Aisha Abdullah Alderremy   +6 more
doaj   +2 more sources

New algorithm for the approximate solution of generalized seventh order Korteweg-Devries equation arising in shallow water waves

Results in Physics, 2021
In the present article, we present for the first time optimal auxiliary function method (OAFM) for partial differential equation (PDEs). To find efficient and precision the proposed method, we take Lax’s seventh order korteweg-de Vries (KdV) and seventh ...
Laiq Zada, Rashid Nawaz, Muhammad Ayaz, Hijaz Ahmad, Hussam Alrabaiah, Yu-Ming Chu   +5 more
doaj   +2 more sources

Closed-Form Almost Periodical Solutions for a Dynamical System Using the Optimal Auxiliary Functions Method

Mathematics
The main aim of our paper is concerning the damped oscillations of 3D dynamical systems, depending on a single physical parameter. This system does not admit Hamilton–Poisson structure but can be explicitly integrated, and the exact parametric solutions ...
Remus-Daniel Ene, Romeo Negrea, Rodica Badarau, Nicolina Pop   +3 more
doaj   +2 more sources

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

Complexity
In this article, we explore the utilization of the Caputo derivative and the Riemann–Liouville (R–L) fractional integral to analyze the optimal auxiliary function method for approximating fractional nonlinear long waves.
Aaqib Iqbal, Rashid Nawaz, Hina Hina, Abdulaziz Garba Ahmad, Homan Emadifar   +4 more
doaj   +2 more sources

Comparative study of fractional Newell–Whitehead–Segel equation using optimal auxiliary function method and a novel iterative approach

AIP Advances
This research explores the solution of the time-fractional Newell–Whitehead–Segel equation using two separate methods: the optimal auxiliary function method and a new iterative method.
Xiao Xin, Ibrar khan, Abdul Hamid Ganie, Ali Akgül, Ebenezer Bonyah, Dowlath Fathima, Badria Almaz Ali Yousif   +6 more
doaj   +3 more sources

Penalty function method for the minimal time crisis problem [PDF]

ESAIM: Proceedings and Surveys, 2021
In this note, we propose a new method to approximate the minimal time crisis problem using an auxiliary control and a penalty function, and show its convergence to a solution to the original problem.
Boumaza Kenza, Bayen Térence, Rapaport Alain   +2 more
doaj   +1 more source

Inverse Optimal Output Regulation for a Class of Uncertain Nonlinear Systems

Journal of Harbin University of Science and Technology, 2023
For a class of nonlinear systems with unknown parameter vector and disturbance, the inverse optimal output regulation problem driven by a linear exosystem is researched.
MENG Guizhi, LÜ Yan
doaj   +1 more source

Rational approximation for solving Fredholm integro-differential equations by new algorithm

Open Physics, 2023
In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs).
Nawaz Rashid, Sumera, Zada Laiq, Ayaz Muhammad, Ahmad Hijaz, Awwad Fuad A., Ismail Emad A. A.   +6 more
doaj   +1 more source

The Optimal Homotopy Asymptotic Method for Solving Two Strongly Fractional-Order Nonlinear Benchmark Oscillatory Problems

Mathematics, 2021
This paper proceeds from the perspective that most strongly nonlinear oscillators of fractional-order do not enjoy exact analytical solutions. Undoubtedly, this is a good enough reason to employ one of the major recent approximate methods, namely an ...
Mohd Taib Shatnawi, Adel Ouannas, Ghenaiet Bahia, Iqbal M. Batiha, Giuseppe Grassi   +4 more
doaj   +1 more source

On the localized and periodic solutions to the time-fractional Klein-Gordan equations: Optimal additive function method and new iterative method

Open Physics, 2023
This investigation explores two numerical approaches: the optimal auxiliary function method (OAFM) and the new iterative method (NIM). These techniques address the physical fractional-order Klein-Gordon equations (FOKGEs), a class of partial differential
Mukhtar Safyan, Abu Hammad Ma’mon, Shah Rasool, Alrowaily Albandari W., Ismaeel Sherif M. E., El-Tantawy Samir A.   +5 more
doaj   +1 more source