Results 1 to 10 of about 45 (34)

A New Extension of Optimal Auxiliary Function Method to Fractional Non-Linear Coupled ITO System and Time Fractional Non-Linear KDV System

Axioms, 2023
In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and the Caputo derivative in the application of the Optimal Auxiliary Function Method (OAFM).
Rashid Nawaz, Aaqib Iqbal, Hina Bakhtiar, Wissal Audah Alhilfi, Nicholas Fewster-Young, Ali Hasan Ali, Ana Danca Poțclean   +6 more
doaj   +3 more sources

Optimal Auxiliary Function Method for Analyzing Nonlinear System of Belousov–Zhabotinsky Equation with Caputo Operator

Axioms, 2023
This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from fractional
Azzh Saad Alshehry, Humaira Yasmin, Muhammad Wakeel Ahmad, Asfandyar Khan, Rasool Shah   +4 more
doaj   +3 more sources

New approximate-analytical solutions to partial differential equations via auxiliary function method

Partial Differential Equations in Applied Mathematics, 2021
In this article, the optimal auxiliary function method (OAFM) is extended to general partial differential equations (PDEs). Our proposed method is highly efficient and provides the means of controlling the approximate solution’s convergence. Illustrative
Laiq Zada, Rashid Nawaz, Kottakkaran Sooppy Nisar, Muhammad Tahir, Mehmet Yavuz, Mohammed K.A. Kaabar, Francisco Martínez   +6 more
doaj   +3 more sources

Optimal auxiliary function method for analyzing nonlinear system of coupled Schrödinger–KdV equation with Caputo operator

Open Physics, 2023
The optimal auxiliary function method (OAFM) is introduced and used in the analysis of a nonlinear system containing coupled Schrödinger–KdV equations, all within the framework of the Caputo operator.
Alshehry Azzh Saad, Yasmin Humaira, Ganie Abdul Hamid, Ahmad Muhammad Wakeel, Shah Rasool   +4 more
doaj   +2 more sources

An extension of optimal auxiliary function method to fractional order high dimensional equations

Alexandria Engineering Journal, 2021
In this article, the new approach called, the optimal auxiliary function method (OAFM) has been extended with the help of the fractional complex transform method (FCTM) to fractional order partial differential equations (PDEs).
Rashid Nawaz, Laiq Zada, Farman Ullah, Hijaz Ahmad, Muhammad Ayaz, Imtiaz Ahmad, Taher A. Nofal   +6 more
doaj   +3 more sources

Modification of the Optimal Auxiliary Function Method for Solving Fractional Order KdV Equations

Fractal and Fractional, 2022
In this study, a new modification of the newly developed semi-analytical method, optimal auxiliary function method (OAFM) is used for fractional-order KdVs equations. This method is called the fractional optimal auxiliary function method (FOAFM).
Hakeem Ullah, Mehreen Fiza, Ilyas Khan, Nawa Alshammari, Nawaf N. Hamadneh, Saeed Islam   +5 more
doaj   +3 more sources

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   +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   +3 more sources

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   +2 more sources

Extension of optimal auxiliary function method to nonlinear Sine Gordon differential equations

Partial Differential Equations in Applied Mathematics
In this paper, the new semi-analytical method called optimal auxiliary function method has been extended for finding the approximate solution of the non-linear Sine Gordon and Burger equations.
Aaqib Iqbal, Rashid Nawaz, Rashid Ashraf, Mehran, Nick Fewster-Young, Hina   +5 more
doaj   +3 more sources