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

Tassaddiq, Asifa; Bhat, Altaf Ahmad; Jain, D. K.; Ali, Farhad

doi:10.3390/sym12030390

Open AccessArticle

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

¹

College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia

²

Department of Mathematical Sciences, Islamic University of Science Technology, Awantipora 192122, India

³

Madhav Institute of Technology and Science, Gwalior 474005, India

⁴

Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan

^*

Authors to whom correspondence should be addressed.

Symmetry 2020, 12(3), 390; https://doi.org/10.3390/sym12030390

Submission received: 13 January 2020 / Revised: 19 February 2020 / Accepted: 25 February 2020 / Published: 3 March 2020

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Abstract

In this paper, we introduce the definitions of Sumudu and Laplace transforms of first and second kind in quantum calculus by using functions of several variables. On account of the general nature of the

(p, q)

-analogue of Aleph-function, a large number of new and known results for these transforms were obtained. Also, we obtain some interesting relationships and identities for these transforms. We also derive some correlations among Aleph function and the above-mentioned integral transforms in quantum calculus.

Keywords: integral transforms; basic hypergeometric functions; q-calculus

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MDPI and ACS Style

Tassaddiq, A.; Bhat, A.A.; Jain, D.K.; Ali, F. On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function. Symmetry 2020, 12, 390. https://doi.org/10.3390/sym12030390

AMA Style

Tassaddiq A, Bhat AA, Jain DK, Ali F. On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function. Symmetry. 2020; 12(3):390. https://doi.org/10.3390/sym12030390

Chicago/Turabian Style

Tassaddiq, Asifa, Altaf Ahmad Bhat, D. K. Jain, and Farhad Ali. 2020. "On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function" Symmetry 12, no. 3: 390. https://doi.org/10.3390/sym12030390

APA Style

Tassaddiq, A., Bhat, A. A., Jain, D. K., & Ali, F. (2020). On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function. Symmetry, 12(3), 390. https://doi.org/10.3390/sym12030390

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

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