Results 1 to 10 of about 82 (55)

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

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

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   +5 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   +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

Analytical and Numerical Analysis of the Squeezed Unsteady MHD Nanofluid Flow in the Presence of Thermal Radiation

Journal of Nanomaterials, Volume 2022, Issue 1, 2022., 2022
In this study, the unsteady squeezing nanofluid flow between two plates with thermal radiation has been investigated. The governing equations of the flow model have been transformed to a set of nonlinear ordinary differential equations (ODEs) from a set of partial differential equations (PDEs) using a suitable similarity variable. The optimal auxiliary
Hakeem Ullah, Muhammad Arif Khan, Mehreen Fiza, Kashif Ullah, Muhammad Ayaz, Seham M. Al-Mekhlafi, Anwar Saeed   +6 more
wiley   +3 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

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

Comparative Evaluation of the Optimal Auxiliary Function Method and Numerical Method to Explore the Heat Transfer between Two Parallel Porous Plates of Steady Nanofluids with Brownian and Thermophoretic Influences

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
In this study, we used the newly established optimal approach, namely, optimal auxilary function method (OAFM) along with the Adams numerical solver technique in order to investigate the heat transfer between two permeable parallel plates of steady nanofluids (HTBTP‐SNFs) through Brownian and thermophoretic consequences.
Hakeem Ullah, Rafaqat Ali Khan, Mehreen Fiza, Saeed Islam, Seham M. Al-Mekhlafi, Arshad Riaz   +5 more
wiley   +1 more source

Comparative Analysis of the Effect of Joule Heating and Slip Velocity on Unsteady Squeezing Nanofluid Flow

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
In this paper, we studied unsteady MHD nanofluid squeezing flow between two parallel plates considering the effect of Joule heating and thermal radiation. The governing equations in the form of partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs) with the help of similarity transformation.
Hakeem Ullah, Hina Khan, Mehreen Fiza, Kashif Ullah, Saeed Islam, Seham M. Al-Mekhlafi, Arshad Riaz   +6 more
wiley   +1 more source