<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We derive formula of Elzaki transform for Hilfer–Prabhakar derivative and its regularized version. The solution of Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative of fractional order is presented in terms of Mittag-Leffler type function. Furthermore, we find the application of the generalized Hilfer-Prabhakar derivative in linear partial differential equation and some problems of Mathematical Physics.</p></abstract>

This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We derive formula of Elzaki transform for Hilfer–Prabhakar derivative and its regularized version. The solution of Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative of fractional order is presented in terms of Mittag-Leffler type function. Furthermore, we find the application of the generalized Hilfer-Prabhakar derivative in linear partial differential equation and some problems of Mathematical Physics.

On the Elzaki transform and its applications in fractional free electron laser equation

Amity Institute of information Technology

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We...

On the Elzaki transform and its applications in fractional free electron laser equation

Published Online: Feb 27, 2020

Page range: 419 - 429

Received: Jan 09, 2019

DOI: https://doi.org/10.2478/ausm-2019-0030

Keywords
Hilfer-Prabhakar fractional derivative, free electron laser equation, Elzaki transform, Mittag-Leffler function, convolution

© 2019 Yudhveer Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Elzaki transform and its applications in fractional free electron laser equation

Published Online: Feb 27, 2020

Page range: 419 - 429

Received: Jan 09, 2019

DOI: https://doi.org/10.2478/ausm-2019-0030

KeywordsHilfer-Prabhakar fractional derivative, free electron laser equation, Elzaki transform, Mittag-Leffler function, convolution

© 2019 Yudhveer Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Hilfer-Prabhakar fractional derivative, free electron laser equation, Elzaki transform, Mittag-Leffler function, convolution