Time Fractional Heat Equation of n + 1-Dimension in Type-1 and Type-2 Fuzzy Environment

Mohapatra, Dhabaleswar; Chakraverty, Snehashish; Alshammari, Mohammad

doi:10.1007/s40815-023-01569-z

Int. J. Fuzzy Syst.

2023

DOI: 10.1007/s40815-023-01569-z

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Time Fractional Heat Equation of n + 1-Dimension in Type-1 and Type-2 Fuzzy Environment

Dhabaleswar Mohapatra,

Snehashish Chakraverty,

Mohammad Alshammari

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2024

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Cited by 4 publications

References 37 publications

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Controllability and Observability of Non-homogeneous Granular Descriptor Fractional Dynamical Systems Applied in Electrical Circuit

Srilekha,

Parthiban

2024

Int. J. Fuzzy Syst.

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Controllability and Observability of Non-homogeneous Granular Descriptor Fractional Dynamical Systems Applied in Electrical Circuit

Srilekha,

Parthiban

2024

Int. J. Fuzzy Syst.

View full text Add to dashboard Cite

Analyzing wave structure and bifurcation in geophysical Boussinesq-type equations

Sahoo,

Chakraverty

2024

Physics of Fluids

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This article investigates the traveling wave solution for a geophysical Boussinesq-type equation that models equatorial tsunami waves. The discussed structure exhibits explicit traveling wave solutions characterized by speeds surpassing the linear propagation speed and small amplitude wave near-field variables. A combination of traveling wave transformation, tanh method, extended tanh method, and a modified form of extended tanh method are implemented, leading to some new traveling wave solutions for the referred nonlinear model. Through the appropriate selection of parameters, the research employs two-dimensional, three-dimensional, and contour plots to showcase the characteristics of specific solutions. The presented visual representation serves as an efficient means to understand the nature of these solutions. This research further extends its investigation by transforming the considered equation into a planar dynamical structure. Through this transformation, all potential phase portraits of the dynamical system are thoroughly examined, utilizing the theory of bifurcation. In addition, this work investigates the modulation of instability in the governing equation using the linear stability analysis function. Importantly, all the newly derived solutions conform to the main equation when substituted into it. The obtained results demonstrate the effectiveness, conciseness, and efficiency of the applied techniques. These strategies have the potential to be useful in scrutinizing more complex models that appear in modern science and engineering.

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Double parametric based solution of fuzzy unconfined aquifer problem using Laplace transforms method

Sahoo,

Behera,

Chakraverty

2024

Physics of Fluids

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The Boussinesq equation describes the model for horizontal water flow in unconfined aquifers without precipitation, a topic that has been extensively studied in the literature. However, the parameters, as well as the initial and boundary conditions, are often assumed to be exact. In reality, these conditions may be incomplete or uncertain due to limited knowledge, insufficient information, or errors introduced by humans or machines. The fuzzy set theory has recently been successfully employed to model such uncertainties. This article investigates the analytical solution of the one-dimensional Boussinesq equation in a fuzzy environment. The objective of this research is to investigate the recharge and discharge of a semi-infinite unconfined aquifer adjacent to a lake. For the present investigation, uncertainties in terms of fuzzy are considered only for the involved initial and boundary conditions of the problem, whereas other parameters are considered as crisp or exact. The analysis employed the double parametric form of a fuzzy number alongside Laplace transform techniques. The obtained solutions were then compared with existing results in specific cases to validate their accuracy.

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Time Fractional Heat Equation of n + 1-Dimension in Type-1 and Type-2 Fuzzy Environment

Cited by 4 publications

References 37 publications

Controllability and Observability of Non-homogeneous Granular Descriptor Fractional Dynamical Systems Applied in Electrical Circuit

Controllability and Observability of Non-homogeneous Granular Descriptor Fractional Dynamical Systems Applied in Electrical Circuit

Analyzing wave structure and bifurcation in geophysical Boussinesq-type equations

Double parametric based solution of fuzzy unconfined aquifer problem using Laplace transforms method

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