Results 51 to 60 of about 541 (198)

Extension of natural transform method with Daftardar-Jafari polynomials for fractional order differential equations

Alexandria Engineering Journal, 2021
This article aims to introduce a new method, called the Natural Transform Iterative Method (NTIM) for the solution of fractional order differential equations. The natural transform iterative method is a modification to the natural transform decomposition
Rashid Nawaz, Nasir Ali, Laiq Zada, Kottakkkaran Sooppy Nisar, M.R. Alharthi, Wasim Jamshed   +5 more
doaj   +1 more source

The Novel Numerical Solutions for Time‐Fractional Fishers Equation

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
A new method for solving time‐fractional partial differential equations (TFPDEs) is proposed in the paper. It is known as the fractional Kamal transform decomposition method (FKTDM). TFPDEs are approximated using the FKTDM. The FKTDM is particularly effective for solving various types of fractional partial differential equations (FPDEs), including time‐
Aslı Alkan, Hasan Bulut, Ercan Çelik, Zine El Abiddine Fellah   +3 more
wiley   +1 more source

Fourth- and fifth-order iterative schemes for nonlinear equations in coupled systems: A novel Adomian decomposition approach

Alexandria Engineering Journal, 2023
In the fields of numerical analysis and applied science, approximating the roots of nonlinear equations is a fundamental and intriguing challenge. With the rapid advancement of computing power, solving nonlinear equations using numerical techniques has ...
Muhammad Saqib, Daud Ahmad, Ahmad N. Al-Kenani, Tofigh Allahviranloo   +3 more
doaj   +1 more source

A modified decomposition

, 1992
The Maclaurin series is quite limited in comparison to the (Adomian) series obtained in the decomposition method. By adding procedures from the decomposition method and the expansion of nonlinearities using the Adomian polynomials, as well as a recent ...
Adomian, G., Rach, R., Meyers, R.E.
core   +1 more source

Improved Analytical Technique Based on Laplace Transform and Homotopy Perturbation Method for Solving Fractional Bratu‐Type Equations

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study presents a modified Laplace transform homotopy perturbation method (MLT‐HPM) for obtaining approximate solutions for fractional‐order Bratu‐type ordinary differential equations involving Caputo fractional derivatives. The proposed modification introduces a specific rule for selecting the initial solution, replacing the conventional random ...
Ibrahim Hailat, Patricia J. Y. Wong
wiley   +1 more source

The dynamics of fractional KdV type equations occurring in magneto-acoustic waves through non-singular kernel derivatives

AIP Advances, 2023
To study magneto-acoustic waves in plasma, we will use a numerical method based on the Natural Transform Decomposition Method (NTDM) to find the approximative solutions of nonlinear fifth-order KdV equations.
Mashael M. AlBaidani, Abdul Hamid Ganie, Adnan Khan   +2 more
doaj   +1 more source

Numerical and Analytical Solutions for a Nonlinear System

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper investigates two nonlinear reaction–diffusion systems: (i) a spatially extended competitive species model and (ii) the FitzHugh–Nagumo system, which serves as a canonical model of excitable media. For the first system, we derive exact closed‐form solutions using the exponential function method; these solutions exhibit spatially periodic ...
Badran Jasim Salim, Dalya Mahmood Merie, Deepali   +2 more
wiley   +1 more source

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim   +2 more
wiley   +1 more source

Iterative procedure for non-linear fractional integro-differential equations via Daftardar–Jafari polynomials

Partial Differential Equations in Applied Mathematics
In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar–Jafari polynomials for solving non-linear problems.
Qasim Khan, Anthony Suen
doaj   +1 more source

Modified decomposition solution of nonlinear partial differential equations

, 1992
Solutions of nonlinear partial differential equations are found using an extended Maclaurin series form of the decomposition method and the Adomian ...
Adomian, G., Rach, R.
core   +1 more source