Note on a $ k $-generalised fractional derivative

Ekta Mittal; Sunil Joshi

doi:10.3934/dcdss.2020045

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2020, Volume 13, Issue 3: 797-804. Doi: 10.3934/dcdss.2020045

This issue Previous Article Analysis of the Fitzhugh Nagumo model with a new numerical scheme Next Article Mathematical modeling approach to the fractional Bergman's model

Note on a $ k $-generalised fractional derivative

Ekta Mittal^1, , and
Sunil Joshi^2, ,

1.
The IIS University, Jaipur, Rajasthan-302020, India
2.
Manipal University Jaipur, Rajasthan-303007, India

Corresponding author: ekta.jaipur@gmail.com; sunil.joshi@jaipur.manipal.edu
Corresponding author: ekta.jaipur@gmail.com; sunil.joshi@jaipur.manipal.edu

Received: April 30, 2018

Revised: July 31, 2018

Published: December 2019

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Abstract

In this paper, we introduce the $ k $-generalised fractional derivatives with three parameters which reduced to $ k $-fractional Hilfer derivatives and $ k $-Riemann-Liouville fractional derivative as an interesting special cases. Further, we have also introduced some presumably new fascinating results which include the image power function, Laplace transform and composition of $ k $-Riemann-Liouville fractional integral with generalized composite fractional derivative. The technique developed in this paper can be used in other situation as well.

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Mathematics Subject Classification: 33B15, 33C05, 26A33.

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References

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