On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics

Muhammad Samraiz; Zahida Perveen; Gauhar Rahman; Kottakkaran Sooppy Nisar; Devendra Kumar

doi:10.3389/fphy.2020.00309

On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics

Muhammad Samraiz, Zahida Perveen, Gauhar Rahman, Kottakkaran Sooppy Nisar, Devendra Kumar

Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-electron laser equation, the generalized time-fractional heat equation, and the generalized fractional kinetic equation using the (k, s)-Hilfer-Prabhakar derivative.

Original language	English
Article number	309
Journal	Frontiers in Physics
Volume	8
DOIs	https://doi.org/10.3389/fphy.2020.00309
State	Published - 23 Oct 2020

Keywords

(k
(k
fractional heat equation
fractional kinetic equation
modified (k
s) fractional integral operator
s)-Hilfer-Prabhakar fractional derivative
s)-Prabhakar fractional derivative

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10.3389/fphy.2020.00309

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abstract = "In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-electron laser equation, the generalized time-fractional heat equation, and the generalized fractional kinetic equation using the (k, s)-Hilfer-Prabhakar derivative.",

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author = "Muhammad Samraiz and Zahida Perveen and Gauhar Rahman and Nisar, \{Kottakkaran Sooppy\} and Devendra Kumar",

note = "Publisher Copyright: {\textcopyright} Copyright {\textcopyright} 2020 Samraiz, Perveen, Rahman, Nisar and Kumar.",

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AU - Samraiz, Muhammad

AU - Perveen, Zahida

AU - Rahman, Gauhar

AU - Nisar, Kottakkaran Sooppy

AU - Kumar, Devendra

PY - 2020/10/23

Y1 - 2020/10/23

N2 - In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-electron laser equation, the generalized time-fractional heat equation, and the generalized fractional kinetic equation using the (k, s)-Hilfer-Prabhakar derivative.

AB - In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-electron laser equation, the generalized time-fractional heat equation, and the generalized fractional kinetic equation using the (k, s)-Hilfer-Prabhakar derivative.

KW - (k

KW - fractional heat equation

KW - fractional kinetic equation

KW - modified (k

KW - s) fractional integral operator

KW - s)-Hilfer-Prabhakar fractional derivative

KW - s)-Prabhakar fractional derivative

UR - https://www.scopus.com/pages/publications/85098586581

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DO - 10.3389/fphy.2020.00309

M3 - Article

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SN - 2296-424X

VL - 8

JO - Frontiers in Physics

JF - Frontiers in Physics

M1 - 309

ER -

On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics

Abstract

Keywords

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