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Series Solutions of Time‐Fractional PDEs by Homotopy Analysis Method [PDF]

International Journal of Differential Equations, 2008
The homotopy analysis method (HAM) is applied to solve linear and nonlinear fractional partial differential equations (fPDEs). The fractional derivatives are described by Caputo′s sense. Series solutions of the fPDEs are obtained. A convergence theorem for the series solution is also given.
Abdulaziz, O., Hashim, I., Saif, A.
core   +7 more sources

Innovative Aboodh-based gractional analytical methods for nonlinear Burgers’ partial differential equations [PDF]

Scientific Reports
This paper explores advanced analytical techniques for solving Burgers’ fractional partial differential equations (PDEs). We focus on the application of two innovative methods: the Aboodh transform iteration method (ATIM) and the Aboodh residual power ...
Naveed Iqbal, Musaad S. Aldhabani, Izatmand Haleemzai, Hasan Nihal Zaidi, Shah Hussain, Safyan Mukhtar, Wael W. Mohammed   +6 more
doaj   +2 more sources

Physics-Informed Neural Networks with Unknown Partial Differential Equations: An Application in Multivariate Time Series [PDF]

Entropy
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: How can models utilize physics or mathematical principles to enhance ...
Seyedeh Azadeh Fallah Mortezanejad, Ruochen Wang, Ali Mohammad-Djafari   +2 more
doaj   +2 more sources

Learning PDE Solution Operator for Continuous Modeling of Time-Series

CoRR, 2023
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make specific assumptions on the type of DEs, making the model specialized for particular problems.
Yesom Park, Jaemoo Choi, Changyeon Yoon, Changhoon Song, Myungjoo Kang   +4 more
openaire   +2 more sources

The solutions of nonlinear fractional partial differential equations by using a novel technique

Open Physics, 2022
In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately.
Alderremy Aisha Abdullah, Khan Hassan, Khan Qasim, Kumam Poom, Aly Shaban, Ahmad Said, Sitthithakerngkiet Kanokwan   +6 more
doaj   +1 more source

Mathematical modelling of unsteady Oldroyd-B fluid flow due to stretchable cylindrical surface with energy transport

Ain Shams Engineering Journal, 2023
The unsteady boundary layer flow and thermal transportation analysis of an incompressible Oldroyd-B nanofluid driven by stretching cylinder is scrutinized with analytically approach in this study.
Muhammad Yasir, Awais Ahmed, Masood Khan, Abdullah Khamis Alzahrani, Zaka Ullah Malik, Ahmed Mohammad Alshehri   +5 more
doaj   +1 more source

Computing power series solutions of a nonlinear PDE system [PDF]

Proceedings of the 2003 international symposium on Symbolic and algebraic computation, 2003
This paper presents a new algorithm to compute the power series solutions of a significant class of nonlinear systems of partial differential equations. The algorithm is very different from previous algorithms to perform this task. Those relie on differentiating iteratively the differential equations to get coefficients of the power series, one at a ...
Evelyne Hubert, Nicolas Le Roux
openaire   +1 more source

A Chebyshev Spectral Collocation Method-Based Series Approach for Boundary Layer Flow and Heat Transfer in a Micropolar Fluid past a Permeable Flat Plate

Journal of Applied Mathematics, 2022
This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly.
T. M. Agbaje, G. Makanda
doaj   +1 more source

Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method

Mathematics, 2022
Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand the complexity of these phenomena. This article introduces a recent attractive analytic-numeric approach to investigate the approximate solutions for nonlinear time fractional partial differential equations by means of ...
Hussam Aljarrah, Mohammad Alaroud, Anuar Ishak, Maslina Darus   +3 more
openaire   +2 more sources

Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems

Advanced Modeling and Simulation in Engineering Sciences, 2023
Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and ...
Pratyush Bhatt, Yash Kumar, Azzeddine Soulaïmani   +2 more
doaj   +1 more source