Results 41 to 50 of about 476 (175)

A Detailed and Comprehensive Account of Fractional Physics‐Informed Neural Networks: From Implementation to Efficiency

Artificial Intelligence for Engineering, EarlyView.
Caputo‐based fPINNs accurately solve fractional ODEs and PDEs while exposing an accuracy–cost trade‐off driven by the history‐dependent fractional derivative. Temporal collocation and shorter time windows are the most effective strategies for improving early‐time accuracy without unnecessary spatial refinement.
Donya Dabiri, Joshua DaRosa, Milad Saadat, Deepak Mangal, Safa Jamali   +4 more
wiley   +1 more source

New Generalised Semi‐Analytical Approach for the Multidimensional Nonlinear Collisional Fragmentation Equations

International Journal for Numerical Methods in Fluids, Volume 98, Issue 8, Page 980-999, August 2026.
This work aims to develop a generalised and efficient semi‐analytical method that combines the Laplace decomposition method with Pade approximation (LDMPA) to solve multidimensional nonlinear integro‐partial differential equation. For a one‐dimension case, explicit (closed‐form) solutions for the number density functions are derived for the first time.
Somveer Keshav, Ashok Das, Sukhjit Singh, Randhir Singh, Mehakpreet Singh   +4 more
wiley   +1 more source

Comparative semi-analytical solutions of Caputo time-fractional Fokker–Planck equations via Laplace transform–based decomposition and iterative methods [PDF]

Iranian Journal of Numerical Analysis and Optimization
In this study, the Laplace Adomian Decomposition Method (LADM) and the Laplace Variational Iteration Method (LVIM) are employed to obtain approximate analytical solutions for both linear and nonlinear time-fractional Fokker-Planck equations (TFFPEs ...
Monowar Hossain, Mohammed Aman Ullah
doaj   +1 more source

Uncertainty Quantification of Analytical Solutions for the Nonlinear Space and Time Fractional Order ϕ4$$ {\phi}^4 $$ Equation Under Fuzziness

Engineering Reports, Volume 8, Issue 7, July 2026.
Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid, Neha Andaleeb Khalid, Baboucarr Ceesay, Zafar Iqbal   +3 more
wiley   +1 more source

On the application of the multistage Laplace Adomian decomposition method to the chaotic Chen system

International Journal of Applied Mathematical Research, 2012
In this paper, Laplace Adomian Decomposition Method (LADM) and the Multistage Laplace Adomian Decomposition Method (MLADM) were applied to obtain solutions to the Chen system for the non-chaotic and chaotic case. The study shows that the LADM only gives reliable results for t
Saheed O. Ajibola, Olusola Tosin Kolebaje, Samuel O. Sedara   +2 more
openaire   +2 more sources

Fractional Novel Analytical Method (FNAM): An Improved Innovative Numerical Scheme to Solve Fractional Differential‐Difference Equations

Engineering Reports, Volume 8, Issue 2, February 2026.
This paper introduces the Fractional Novel Analytical Method (FNAM), a Taylor‐series‐based technique for approximating nonlinear fractional differential‐difference equations. Built on the Caputo derivative, FNAM achieves rapid convergence without relying on Adomian polynomials, perturbation schemes, or transform methods.
Uroosa Arshad, Mariam Sultana, Homan Emadifar, Atul Kumar   +3 more
wiley   +1 more source

A Decompositional Approach for Two‐Dimensional, Two‐Phase, Nonlinear Inverse Stefan Problems Using the Method of Fundamental Solutions

Studies in Applied Mathematics, Volume 156, Issue 2, February 2026.
ABSTRACT In this paper, we propose a decompositional (phase‐wise split) approach to solve a two‐dimensional, two‐phase (solid and liquid, say), nonlinear inverse Stefan problem. The first step is to approximate the unknown moving boundary between the two phases and the Stefan condition on that boundary using the overspecified boundary and initial data ...
Gujji Murali Mohan Reddy, Phalguni Nanda, Michael Vynnycky   +2 more
wiley   +1 more source

Solution of an extraordinary differential equation by Adomian decomposition method

Journal of Applied Mathematics, 2004
The aim of the present analysis is to apply the Adomian decomposition method for the solution of a fractional differential equation as an alternative method of Laplace transform.
S. Saha Ray, R. K. Bera
doaj   +1 more source

On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions

Complexity, 2020
In this paper, the fractional view analysis of the Keller–Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work.
Haobin Liu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu   +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