Results 51 to 60 of about 334 (167)

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

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

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton‐like structures, and clearly reveals the critical ...
Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed, Rajesh Kumar   +3 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

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

On the Coupling of Auxiliary Parameter, Adomian's Polynomials and Correction Functional [PDF]

Mathematical and Computational Applications, 2011
In this paper, we apply He’s variational iteration method (VIM) coupled with an auxiliary parameter and Adomian’s polynomials which proves very effective to control the convergence region of approximate solution. The proposed algorithm is tested on generalized Hirota–Satsuma coupled KdV equation and numerical results explicitly reveal the complete ...
Hosseini, M., Mohyud-Din, Syed, Ghaneai, H.   +2 more
openaire   +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

A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations

Alexandria Engineering Journal
This paper introduces a numerical approach by generalizing Legendre wavelets for solving nonlinear Caputo–Hadamard fractional differential equations. The methodology involves the extension of classical Legendre wavelets, namely the generalized Legendre ...
Umer Saeed, Mujeeb ur Rehman
doaj   +1 more source

Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations

Journal of Low Frequency Noise, Vibration and Active Control, 2019
In this work, the variational iteration algorithm-I with an auxiliary parameter is used for the analytical treatment of the wave equations and wave-like vibration equations.
Hijaz Ahmad, Tufail A. Khan
doaj   +1 more source