Results 1 to 10 of about 268,057 (260)

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   +4 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   +4 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   +4 more sources

Extension of optimal auxiliary function method to non-linear fifth order lax and Swada-Kotera problem

Alexandria Engineering Journal, 2023
In this article, a semi-analytical approach known as the optimal auxiliary function method is extended to the approximate solution of non-linear partial differential equations.
Rashid Nawaz, Hina Hina, Aaqib Iqbal, Abdulaziz Garba Ahmad, Rashid Ashraf, Homan Emadifar   +5 more
doaj   +4 more sources

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

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   +6 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   +4 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   +4 more sources

A New Hybrid Optimal Auxiliary Function Method for Approximate Solutions of Non-Linear Fractional Partial Differential Equations

Fractal and Fractional, 2023
This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville’s fractional integral and the Caputo derivative.
Rashid Ashraf, Rashid Nawaz, Osama Alabdali, Nicholas Fewster-Young, Ali Hasan Ali, Firas Ghanim, Alina Alb Lupaş   +6 more
doaj   +4 more sources

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   +4 more sources

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