Application of -HATM over Fractional in Time Model for Advection-Dispersion Equation with Variable Migration Parameters
Publication: Journal of Engineering Mechanics
Volume 149, Issue 6
Abstract
In this article, an extended and more generalized method of homotopy analysis method (HAM), known as q-homotopy analysis transform method (-HATM) is employed to develop solutions for highly nonlinear form of various time-fractional advection-dispersion models (TFADE). The proposed methodology of -HATM is a conjunction of two different strong methodologies, that are HAM and Laplace transform technique (LTT) which makes the scheme much more capable to develop the convergent series solutions for differential equations with high nonlinearity. In this work, two different examples are constructed for the nonlinear time-fractional form of dispersion models corresponding to distance dependent dispersion and velocity components and also for the time dependent decay rate system and solutions are constructed by using -HATM in generalized form. The graphical comparison is made for different types of variable functions and also for the different fractional order indexes. Prominent impact of fractional derivative indexes is significantly observed over both the examples of dispersion models. Hence, proposed examples shows that the -HATM is much convenient to handle the nonlinear systems of fractional models.
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Data Availability Statement
The data and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors wish to acknowledge the reviewers for their valuable comments and suggestions.
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Published In
Journal of Engineering Mechanics
Volume 149 • Issue 6 • June 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Apr 12, 2022
Accepted: Feb 3, 2023
Published online: Apr 7, 2023
Published in print: Jun 1, 2023
Discussion open until: Sep 7, 2023
ASCE Technical Topics:
- Advection
- Biological processes
- Decomposition
- Differential equations
- Engineering fundamentals
- Environmental engineering
- Equations (by type)
- Finite difference method
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Hydrologic engineering
- Laplace transform
- Mathematics
- Measurement (by type)
- Methodology (by type)
- Nonlinear analysis
- Numerical methods
- Parameters (statistics)
- Statistics
- Structural analysis
- Structural engineering
- Time dependence
- Waste management
- Water and water resources
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