Fareeha transform: A new generalized Laplace transform

Khan, Fareeha Sami; Khalid, M.

doi:10.1002/mma.9167

Math Methods in App Sciences

2023

DOI: 10.1002/mma.9167

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Fareeha transform: A new generalized Laplace transform

Fareeha Sami Khan

M. Khalid

Abstract: In this paper, a new integral-type transformation is being introduced, which is the generalization of Laplace and Fourier transform. This integral transform is named as "Fareeha transform." It is successfully applied on ordinary differential equation to show its efficacy and simplicity. Also, the possible applications of Fareeha transform in control theory, electric circuits, and data compression have been discussed in detail.

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Cited by 3 publications

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Integral transformation for nonlinear oscillators

Dong,

Ou,

et al. 2024

Journal of Low Frequency Noise, Vibration and Active Control

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This paper introduces a generalized integral transform that encompasses the Laplace, Fourier, and numerous contemporary integral transforms as particular instances, while preserving their defining characteristics. Secondly, we propose the application of the generalized integral transform in the variational iteration method for the straightforward identification of the Lagrange multiplier, thus enabling the resolution of nonlinear oscillator problems. Finally, we present a series of illustrative examples to demonstrate the efficacy of this approach.

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Integral transformation for nonlinear oscillators

Dong,

Ou,

et al. 2024

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

show abstract

Beyond Laplace and Fourier transforms: Challenges and future prospects

He,

Anjum,

et al. 2023

Therm sci

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Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform and other transforms, e.g., Elzaki Sumudu transform, Aboodh transform, Pourreza transform and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various nonlinear problems, opening a new window for nonlinear science.

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Fareeha Transform Performance In Solving Fractional Differential Telegraph Equations Combining Adomian Decomposition Method

Tuan,

Koonprasert,

Meesad

2024

Wseas Transactions on Systems and Control

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Transformations have successfully outperformed a significant role in solving differential equations and have been applied in large-scale aspects of science. Fareeha transform has been illustrated effectively in data compression based on containing more information of the transform. In this paper, we expand the fractional Fareeha transform in the Caputo derivative sense combining the Adomian Decomposition Method to seek the solutions of fractional differential telegraph equations. The results of practical utilization have also been significantly shown successful in solving fractional telegraph differential equations.

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Fareeha transform: A new generalized Laplace transform

Cited by 3 publications

References 11 publications

Integral transformation for nonlinear oscillators

Integral transformation for nonlinear oscillators

Beyond Laplace and Fourier transforms: Challenges and future prospects

Fareeha Transform Performance In Solving Fractional Differential Telegraph Equations Combining Adomian Decomposition Method

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