Certain results related to the N-transform of a certain class of functions and differential operators

Al‐Omari, Shrideh

doi:10.1186/s13662-017-1457-y

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…Hence, the relation between the natural, Laplace, and Sumudu transforms is a symmetric relation. Next, Al-Omari [9] extended to the q-natural transform which is defined over the sets B and C, respectively,…”

Section: Some Properties Of the (P Q)-natural Transformmentioning

confidence: 99%

“…In 2014, Chung et al [20] studied the q-analogues of the Laplace transform and pinpointed some distinct properties of the q-Laplcae transform to further the investigation. In 2018, Al-Omari [9] proposed the q-analogues of the natural transform on many functions of a special kind with the first kind and the second kind, and some of their respective properties. In 2020, he proposed the q-analogues and properties of the Laplace-type integral operator in the quantum calculus [10].…”

Section: Introductionmentioning

confidence: 99%

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On a system of ( p , q ) -analogues of the natural transform for solving ( p , q ) -differential equations

Jirakulchaiwong¹,

Nonlaopon²,

Tariboon³

et al. 2022

J. Math. Computer Sci.

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In this work, we apply the concept of (p, q)-calculus or post quantum calculus to establish the definitions of (p, q)-analogues of the natural transform of the first and second kind, which is a symmetric relation between (p, q)-analogues of the natural, Laplace, and Sumudu transforms. Moreover, as a result of the convolution theorem, some properties and some functions present in the table of (p, q)-analogues of the natural transform are discussed. Also, we apply them to solve higher order (p, q)-IVP with constants and coefficients, and to show the performance and effectiveness of the proposed transform.

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Section: Some Properties Of the (P Q)-natural Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On a system of ( p , q ) -analogues of the natural transform for solving ( p , q ) -differential equations

Jirakulchaiwong¹,

Nonlaopon²,

Tariboon³

et al. 2022

J. Math. Computer Sci.

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“…The fractional q-calculus is the q-extension of the ordinary fractional calculus. Integral operators have attained their popularity due to their wide range of applications in various fields of science and engineering [17][18][19][20][21][22] and [23][24][25][26][27][28][29][30][31][32][33][34]. In [35,36] Al-Salam and Agarwal studied certain q-fractional integrals and derivatives.…”

Section: Introductionmentioning

confidence: 99%

A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

2021

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This paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various types of q-Bessel functions and some power series of special type. It has been obtained for basic q-generating series, q-exponential and q-trigonometric functions as well. Various results and corollaries are provided as an application to this theory.

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“…where u and v are the transform variables. The GNT transform corresponds to the NT for α = 0 [8] and to the Stieltjes transform for u = 0 [9]. On top of that, it corresponds to the Laplace transform [10]…”

Section: Introductionmentioning

confidence: 99%

Certain fundamental properties of generalized natural transform in generalized spaces

Al‐Omari

Aracı

2021

Adv Differ Equ

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This paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

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Certain results related to the N-transform of a certain class of functions and differential operators

Cited by 5 publications

References 12 publications

On a system of ( p , q ) -analogues of the natural transform for solving ( p , q ) -differential equations

On a system of ( p , q ) -analogues of the natural transform for solving ( p , q ) -differential equations

A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

Certain fundamental properties of generalized natural transform in generalized spaces

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