Multiplicative Laplace transform in q−calculus

Yilmazer, Mehmet; Yilmaz, Emrah; Goktas, Sertac; Et, Mikail

doi:10.2298/fil2318859y

Filomat

2023

DOI: 10.2298/fil2318859y

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Multiplicative Laplace transform in q−calculus

Mehmet Yilmazer,

Emrah Yilmaz,

Sertac Goktas

et al.

Abstract: In this study, we introduce q-(or q-multiplicative) Laplace transform by means of q-integral. Some properties of q-Laplace transform are presented. Also, q-Laplace transform can be utilized for solving q*-linear differential equations.

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2024

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Non-Newtonian Pell and Pell-Lucas numbers

Yağmur

2024

Journal of New Results in Science

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In the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively. In non-Newtonian calculus, we study some significant identities and formulas for classical Pell and Pell-Lucas numbers. Therefore, we derive some relations with non-Newtonian Pell and Pell-Lucas numbers. Furthermore, we investigate some properties of non-Newtonian Pell and Pell-Lucas numbers, including Catalan-like identities, Cassini-like identities, Binet-like formulas, and generating functions.

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Non-Newtonian Pell and Pell-Lucas numbers

Yağmur

2024

Journal of New Results in Science

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Multiplicative Laplace transform in q−calculus

Abstract: In this study, we introduce q-(or q-multiplicative) Laplace transform by means of q-integral. Some properties of q-Laplace transform are presented. Also, q-Laplace transform can be utilized for solving q*-linear differential equations.

Cited by 1 publication

References 27 publications

Non-Newtonian Pell and Pell-Lucas numbers

Non-Newtonian Pell and Pell-Lucas numbers

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Multiplicative Laplace transform in q−calculus

Abstract: In this study, we introduce q*-(or q-multiplicative) Laplace transform by means of q*-integral. Some properties of q*-Laplace transform are presented. Also, q*-Laplace transform can be utilized for solving q*-linear differential equations.

Cited by 1 publication

References 27 publications

Non-Newtonian Pell and Pell-Lucas numbers

Non-Newtonian Pell and Pell-Lucas numbers

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Product

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Abstract: In this study, we introduce q-(or q-multiplicative) Laplace transform by means of q-integral. Some properties of q-Laplace transform are presented. Also, q-Laplace transform can be utilized for solving q*-linear differential equations.