New theoretical results and applications on conformable fractional Natural transform

Al–Zhour, Zeyad; Al-Mutairi, Nouf; Alrawajeh, Fatimah Abdulrahman; Alkhasawneh, Raed

doi:10.1016/j.asej.2020.07.006

Cited by 12 publications

(4 citation statements)

References 41 publications

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“…Remark 25 The results of this section contain as a particular case, those of, 54 = that is, the conformable case, the results obtained in 18,20,22,52,56 can be generalized with our kernel.…”

Section: Theorem 24 the System (18) Is Is Asymptotically Stable If An...mentioning

confidence: 63%

On the generalized laplace transform and applications

Nápoles Valdés

2022

PAIJ

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In this work we present the main properties of the Generalized Laplace Transform, recently defined, and we show some applications. Laplace’s transformation has been very useful in the studies of engineering, mathematics, physics, among other scientific areas. One of the main mathematical areas where it has many applications is in the topic of differential equations and their solution methods. In this paper, we study the stability and analysis of linear systems with the Generalized Laplace Transform.

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Section: Theorem 24 the System (18) Is Is Asymptotically Stable If An...mentioning

confidence: 63%

On the generalized laplace transform and applications

Nápoles Valdés

2022

PAIJ

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“…Finally, as an application, we solve a non-homogeneous fractional di erential equation with variable coe cients using the conformable Laplace transform. For further results on conformable Laplace transform, see [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness Study of the Conformable Laplace Transform

Younis

Bouchenak

AlJazzazi

et al. 2022

Journal of Mathematics

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This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Laplace transform for some functions. The uniqueness is also established in order to determine the inverse of conformable Laplace transform for functions. Moreover, we present a table of the conformable Laplace transform of the usual functions. Finally, as an application, we use the conformable Laplace transform for solving some fractional differential equations.

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“…In the last two decades, many integral transforms in the class of Laplace-typed integral transform are introduced, such as Sumudu transform, Elzaki transform, natural transform, Aboodh transform, Mohand transform, G α -transform, HY-transform, and Kamal transform. These transforms have been used for solving different types of integral equations, ordinary differential equations, partial differential equations, and fractional differential equations, see [1,3,15,22,37,42,45] for more details.…”

Section: Introductionmentioning

confidence: 99%