Results 51 to 60 of about 111,766 (161)

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

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

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

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

Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations [PDF]

, 2013
We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations.
Clarkson, Peter
core   +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

Modeling and Complexity Analysis of Fuzzy‐Fractional Chaotic Systems Using Deep Neural Networks

Complexity, Volume 2026, Issue 1, 2026.
Nonlinear dynamical systems exhibiting chaos, memory and uncertainty effects play a vital role in the modeling of complex phenomena in science and engineering. Due to the rapid growing of development in machine learning and artificial intelligence, data‐driven methods have been widely used for predicting and analysing nonlinear dynamical systems ...
Shamaila Waheed, Mubashir Qayyum, Aiedh Mrisi Alharthi, Syed Tauseef Saeed, Gilbert Chambashi, Jesus Manuel Munoz-Pacheco   +5 more
wiley   +1 more source

On the Locally Compact Hausdorff Property in the Analytical Solutions and Stability Analysis of the Caputo Fractional Belousov–Zhabotinsky System

Complexity, Volume 2026, Issue 1, 2026.
The fractional Belousov–Zhabotinsky system (BZS) is an important reaction–diffusion model used to describe oscillatory chemical reactions, pattern formation, and memory‐dependent dynamical processes arising in chemistry and related applied sciences. The main objective of this study is to investigate the analytical properties of the fractional BZS and ...
Faten H. Damag, Mohammad Alshammari, Amin Saif, Yusuf Zeren, Mohammed S. Alsharafi, Shikha Binwal   +5 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

Wavelet Collocation Method Based on Biorthogonal Flatlet Multiwavelet and Its Application in Solving the Singular BVPs

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
The main focus of our work is to provide a computationally efficient approximate algorithm for finding a numerical solution of singular boundary value problems (SBVPs). For this purpose, we apply a biorthogonal flatlet multiwavelet collocation method (BFMCM) to solve numerically. This is performed by approximating functions using a BFMCM.
Maryam Mohseni, Davood Rostamy, Md. Kamrujjaman   +2 more
wiley   +1 more source