A fractional-order framework for investigating groundwater depletion under environmental and human pressures

Gnanasakthivel Hamsavarthini; Chokkalingam Ravichandran; Fahad Aljuaydi; Kottakkaran Sooppy Nisar

doi:10.1007/s12190-025-02514-z

A fractional-order framework for investigating groundwater depletion under environmental and human pressures

Gnanasakthivel Hamsavarthini
, Chokkalingam Ravichandran
, Fahad Aljuaydi
, Kottakkaran Sooppy Nisar

Mathematics

Bharathiar University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

A fractional-order model with Caputo derivatives is developed to study the water dynamics with an emphasis on the interactions between atmospheric water, surface water, and groundwater. The model considers significant environmental issues such as pollution, deforestation, and frequent water pumping and assesses their effects on groundwater levels. Conditions for the existence, and boundedness of solutions are also studied. The steady-state solutions of the system are identified, and their stability is used Lyapunov’s direct method to determine boundedness, positivity, and stability of solutions. The study employed numerical models to analyze the effects of human pressure.

Original language	English
Pages (from-to)	1061-1077
Number of pages	17
Journal	Journal of Applied Mathematics and Computing
Volume	71
Issue number	Suppl 1
DOIs	https://doi.org/10.1007/s12190-025-02514-z
State	Published - Sep 2025

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 6 Clean Water and Sanitation

Keywords

Fractional calculus
Lyapunov direct method
Mathematical modelling
Numerical simulation

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10.1007/s12190-025-02514-z

Cite this

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title = "A fractional-order framework for investigating groundwater depletion under environmental and human pressures",

abstract = "A fractional-order model with Caputo derivatives is developed to study the water dynamics with an emphasis on the interactions between atmospheric water, surface water, and groundwater. The model considers significant environmental issues such as pollution, deforestation, and frequent water pumping and assesses their effects on groundwater levels. Conditions for the existence, and boundedness of solutions are also studied. The steady-state solutions of the system are identified, and their stability is used Lyapunov{\textquoteright}s direct method to determine boundedness, positivity, and stability of solutions. The study employed numerical models to analyze the effects of human pressure.",

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author = "Gnanasakthivel Hamsavarthini and Chokkalingam Ravichandran and Fahad Aljuaydi and Nisar, \{Kottakkaran Sooppy\}",

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AU - Hamsavarthini, Gnanasakthivel

AU - Ravichandran, Chokkalingam

AU - Aljuaydi, Fahad

AU - Nisar, Kottakkaran Sooppy

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.

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N2 - A fractional-order model with Caputo derivatives is developed to study the water dynamics with an emphasis on the interactions between atmospheric water, surface water, and groundwater. The model considers significant environmental issues such as pollution, deforestation, and frequent water pumping and assesses their effects on groundwater levels. Conditions for the existence, and boundedness of solutions are also studied. The steady-state solutions of the system are identified, and their stability is used Lyapunov’s direct method to determine boundedness, positivity, and stability of solutions. The study employed numerical models to analyze the effects of human pressure.

AB - A fractional-order model with Caputo derivatives is developed to study the water dynamics with an emphasis on the interactions between atmospheric water, surface water, and groundwater. The model considers significant environmental issues such as pollution, deforestation, and frequent water pumping and assesses their effects on groundwater levels. Conditions for the existence, and boundedness of solutions are also studied. The steady-state solutions of the system are identified, and their stability is used Lyapunov’s direct method to determine boundedness, positivity, and stability of solutions. The study employed numerical models to analyze the effects of human pressure.

KW - Fractional calculus

KW - Lyapunov direct method

KW - Mathematical modelling

KW - Numerical simulation

UR - https://www.scopus.com/pages/publications/105005113659

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DO - 10.1007/s12190-025-02514-z

M3 - Article

AN - SCOPUS:105005113659

SN - 1598-5865

VL - 71

SP - 1061

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JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - Suppl 1

ER -

A fractional-order framework for investigating groundwater depletion under environmental and human pressures

Abstract

UN SDGs

Keywords

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