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2021•IOP Conference Series Materials Science and EngineeringOpen access

Some new applications of β-Laplace integral transform

Amit Gaur, Garima Agarwal

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Abstract

Abstract The β-Laplace integral transform(β-LIT) has been introduced recently by Gaur et. al. which is a generalization of Laplace transform. This new β-LIT shows some special properties over Laplace integral transform. In the current paper, we investigate the applicability of the β-LIT technique to solve partial differential equation such as initial value problem of first order and second order PDE, wave equation, Diffusion equation, Potential and current equation, Heat conduction equation, Axisymmetric Heat conduction equation, Inhomogeneous partial differential equation, inhomogeneous wave equation, Stroke and Rayleigh problem in fluid dynamics and illustrate by some examples.

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Abstract The β-Laplace integral transform(β-LIT) has been introduced recently by Gaur et. al. which is a generalization of Laplace transform. This new β-LIT shows some special properties over Laplace integral transform. In the current paper, we investigate the applicability of the β-LIT technique to solve partial differential equation such as initial value problem of first order and second order PDE, wave equation, Diffusion equation, Potential and current equation, Heat conduction equation, Axisymmetric Heat conduction equation, Inhomogeneous partial differential equation, inhomogeneous wave equation, Stroke and Rayleigh problem in fluid dynamics and illustrate by some examples.

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Available abstract

Abstract The β-Laplace integral transform(β-LIT) has been introduced recently by Gaur et. al. which is a generalization of Laplace transform. This new β-LIT shows some special properties over Laplace integral transform. In the current paper, we investigate the applicability of the β-LIT technique to solve partial differential equation such as initial value problem of first order and second order PDE, wave equation, Diffusion equation, Potential and current equation, Heat conduction equation, Axisymmetric Heat conduction equation, Inhomogeneous partial differential equation, inhomogeneous wave equation, Stroke and Rayleigh problem in fluid dynamics and illustrate by some examples.

Key concepts: Green's function for the three-variable Laplace equation, Laplace's equation, Partial differential equation, Heat equation, Laplace transform, Laplace transform applied to differential equations, First-order partial differential equation, Mathematics

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