New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations

Maitama, Shehu; Zhang, Weidong

doi:10.28924/2291-8639-17-2019-167

Cited by 26 publications

(19 citation statements)

References 32 publications

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“…A generalization of the Laplace and Sumudu integral transforms, the Shehu transformation was first introduced by Maitama and Zhao in 2019 [26]. The authors used it to solve differential equations.…”

Section: Shehu Transformationmentioning

confidence: 99%

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A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

Al-Sadi,

Al-Saif

2023

MMEP

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This study introduces a novel method aimed at deriving approximate solutions for diffusive prey-predator systems. The proposed method seeks to circumvent the limitations of extant techniques, which frequently grapple with obtaining accurate analytical solutions and managing intricate computational operations. This new approach amalgamates the Shehu transformation, Akbari-Ganji's method, and Padé Approximant to facilitate a more precise and efficient solution. The accuracy, efficiency, and effectiveness of the proposed method are assessed through the analysis of two exemplar cases in one-and two-dimensional spaces. Results gleaned from the novel method underscore its superior accuracy and efficiency compared to traditional methods used for approximating analytical solutions to similar problems. Further, the utilization of infographics and tables elucidates the significance, validity, and indispensability of the proposed approach. This research augments our comprehension of biological systems and their interactions with the environment, thereby presenting a valuable contribution to the academic discourse.

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Section: Shehu Transformationmentioning

confidence: 99%

“…Meanwhile, the Padé approximation, crafted by Henri Padé in 1890, optimizes the accuracy and convergence of solutions by approximating a function near a specific point [25]. More recent is the Shehu transformation, introduced by Maitama and Zhao in 2019 [26].…”

Section: Introductionmentioning

confidence: 99%

A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

Al-Sadi,

Al-Saif

2023

MMEP

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“…The Shehu transform was defined by Shehu Maitama [9,19], in 2019. In this section, we give some basics definitions and properties of this transform.…”

Section: Shehu Transformmentioning

confidence: 99%

“…The objective of the present study is to combine two powerful methods, variational iteration method [5][6][7]15] and Shehu transform [2,9] to get a faster method to solve nonlinear fraction partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Shehu Variational Iteration Method For Solve Some Fractional Differential Equations

Boulekhras

Belghaba

2022

Comm. Math. Appl.

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“…Researchers have employed a variety of integral transforms (such as the Sumudu transform and Laplace transform) as well as other decomposition strategies to deal with these kinds of non-linear FDEs, as has already been discussed. The Shehu transform (ST) is another integral transformation that was recently presented by Maitama et al [28], which is a generalization of the Laplace and Sumudu integral transforms [29]. Shehu and Zhao [28] used ST to resolve a large number of non-linear ordinary as well as partial differential equations of integer order.…”

Section: Introductionmentioning

confidence: 99%

Solving Nonlinear Fractional Differential Equations by Using Shehu Transform and Adomian Polynomials

Singh,

Pippal

2024

Contemp. Math.

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The current article provides a detailed analysis of the solution of non-linear ordinary differential equations of fractional and non-fractional order in series forms using the Shehu transform (ST) and the Adomian decomposition method (ADM), also known as the Shehu transform Adomian decomposition method (STADM). Previously, these methods were used to solve differential equations of integer order as well as a very small number of ordinary and fractional differential equations (FDEs). The Caputo's operator is used in a number of well-known FDEs, including the logistic equation, the Van der Pole equation, and other non-fractional order differential equations like the nonlinear Bratu type equation. It is noted that all of the example issues had series solutions thanks to STADM. Plotting the graph for several series terms of the series solution demonstrates how the approximate solution tends to the closed form solution. In some example problems the impact of α is shown.

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New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations

Cited by 26 publications

References 32 publications

A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

Shehu Variational Iteration Method For Solve Some Fractional Differential Equations

Solving Nonlinear Fractional Differential Equations by Using Shehu Transform and Adomian Polynomials

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