A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation

Gorty, V. R. Lakshmi

doi:10.1515/tmj-2015-0004

Cited by 1 publication

(1 citation statement)

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“…Some of these look very much like a regular Laplace transform [1,30,25,44], while others look quite different [45,15,47]. The k-Laplace transforms [47] look a bit more like Mellin transforms, while the definitions used by Sharma [45], Deshmukh and Gudadhe [15], and Gorty [18] involve cotangents and cosecants in the exponential Laplace kernel. To be sure, the regular Laplace transform has also been used to tackle fractional differential equations, often resulting in a Mittag-Leffler expansion solution [39].…”

Section: Integral Transformsmentioning

confidence: 99%

On the nature of the conformable derivative and its applications to physics

Anderson,

Camrud,

Ulness

2018

Preprint

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The purpose of this work is to show that the Khalil and Katagampoula conformable derivatives are equivalent to the simple change of variables x → x α /α, where α is the order of the derivative operator, when applied to differential functions. Although this means no "new mathematics" is obtained by working with these derivatives, it is a second purpose of this work to argue that there is still significant value in exploring the mathematics and physical applications of these derivatives. This work considers linear differential equations, self-adjointness, Sturm-Liouville systems, and integral transforms. A third purpose of this work is to contribute to the physical interpretation when these derivatives are applied to physics and engineering. Quantum mechanics serves as the primary backdrop for this development.

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