On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function

Tassaddiq, Asifa; Bhat, Altaf Ahmad; Jain, Deepak Kumar; Ali, Farhad

doi:10.3390/sym12030390

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…Laplace transform [40,[45][46][47] Definition of quantum Laplace transform and its properties [38][39][40][41][42][43][44][45][46][47][48] Using the Laplace transform to solve engineering problems 48 Report an incorrect use of the Laplace transform to solve a specific type of the Schrödinger equation Englefield (1968) used the Laplace transform method to examine the problem of the one-dimensional quantum harmonic oscillator [37]. Further, it has been shown that the wave function which defines a quantum mechanical system can be represented by the Laplace transform of a certain distribution and the result of a certain subclass [38].…”

Section: Mathematical Tool References Objectivementioning

confidence: 99%

“…Then, using q-integral definition on quantum analogs, Alp & Sarikaya (2023) described the 𝑞 ̅-Laplace transform and some of its properties along with formulas of q-Laplace transform and applications [46]. Sumudu and Laplace transforms of the first and second kind have been defined in quantum calculus for functions of several variables, and some interesting relationships and identities for these transforms are described [47]. Correlations among Aleph functions and the above-mentioned integral transforms in quantum calculus have been derived.…”

Section: Mathematical Tool References Objectivementioning

confidence: 99%

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A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

et al. 2022

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Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PDF

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Section: Mathematical Tool References Objectivementioning

confidence: 99%

Section: Mathematical Tool References Objectivementioning

confidence: 99%

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

et al. 2022

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“…In 2019, Sadjang [42] studied the (p, q)-analogues of the Sumudu transform and gave some properties to solve (p, q)-difference equations. In 2020, Tassaddiq et al [47] proposed (p, q)-analogues of Laplace and (p, q)-analogues of Sumudu transforms with (p, q)-Aleph function. Recently, Jirakulchaiwong et al [31] established (p, q)-analogues of Laplace-type integral transforms and use some obtained properties to apply some (p, q)-differential equations.…”

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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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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“…Recently, many works established Laplace integral transforms of special functions like Gauss's and Kummer's functions [29], generalized hypergeometric functions [30,31], Aleph-Functions [32], and Bessel functions [33]. Whereas, some formulas corresponding to integral transforms of orthogonal matrix polynomials are little known and traceless in the literature.…”

Section: Introductionmentioning

confidence: 99%

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

Hidan

Akel

Boulaaras

et al. 2021

Journal of Function Spaces

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Recently, the applications and importance of integral transforms (or operators) with special functions and polynomials have received more attention in various fields like fractional analysis, survival analysis, physics, statistics, and engendering. In this article, we aim to introduce a number of Laplace and inverse Laplace integral transforms of functions involving the generalized and reverse generalized Bessel matrix polynomials. In addition, the current outcomes are yielded to more outcomes in the modern theory of integral transforms.

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On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function

Cited by 4 publications

References 20 publications

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

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

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

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