A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator

Sunil Kumar; Surath Ghosh; Mansour S.M. Lotayif; Bessem Samet

doi:10.1016/j.aej.2020.04.019

A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator

Sunil Kumar
, Surath Ghosh
, Mansour S.M. Lotayif
, Bessem Samet

National Institute of Technology Jamshedpur
Applied Science University
King Saud University

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

68 Scopus citations

Abstract

This endeavour provides a new instance of understanding the velocity of a particle in Brownian motion, using the Fokker-Plank equation. Our treatment is based on the new mathematical tool invoked by Yang-Abdel-Aty-Cattani (YAC) to solve the fractional derivative on Fokker-Plank equation. The HPTM and RPSMs, are used to obtain the solution in terms of Prabhakar function. Numerical examples to extend these ideas and to establish the capability and truthfulness of the proposed method, which makes use of YAC-fractional derivative, is also briefly sketched.

Original language	English
Pages (from-to)	1435-1449
Number of pages	15
Journal	Alexandria Engineering Journal
Volume	59
Issue number	3
DOIs	https://doi.org/10.1016/j.aej.2020.04.019
State	Published - Jun 2020
Externally published	Yes

Keywords

Fokker-Plank equation
HPTM
New fractional derivative
RPSM
Robotnov fractional exponential function

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10.1016/j.aej.2020.04.019

Cite this

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title = "A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator",

abstract = "This endeavour provides a new instance of understanding the velocity of a particle in Brownian motion, using the Fokker-Plank equation. Our treatment is based on the new mathematical tool invoked by Yang-Abdel-Aty-Cattani (YAC) to solve the fractional derivative on Fokker-Plank equation. The HPTM and RPSMs, are used to obtain the solution in terms of Prabhakar function. Numerical examples to extend these ideas and to establish the capability and truthfulness of the proposed method, which makes use of YAC-fractional derivative, is also briefly sketched.",

keywords = "Fokker-Plank equation, HPTM, New fractional derivative, RPSM, Robotnov fractional exponential function",

author = "Sunil Kumar and Surath Ghosh and Lotayif, \{Mansour S.M.\} and Bessem Samet",

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year = "2020",

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AU - Kumar, Sunil

AU - Ghosh, Surath

AU - Lotayif, Mansour S.M.

AU - Samet, Bessem

PY - 2020/6

Y1 - 2020/6

N2 - This endeavour provides a new instance of understanding the velocity of a particle in Brownian motion, using the Fokker-Plank equation. Our treatment is based on the new mathematical tool invoked by Yang-Abdel-Aty-Cattani (YAC) to solve the fractional derivative on Fokker-Plank equation. The HPTM and RPSMs, are used to obtain the solution in terms of Prabhakar function. Numerical examples to extend these ideas and to establish the capability and truthfulness of the proposed method, which makes use of YAC-fractional derivative, is also briefly sketched.

AB - This endeavour provides a new instance of understanding the velocity of a particle in Brownian motion, using the Fokker-Plank equation. Our treatment is based on the new mathematical tool invoked by Yang-Abdel-Aty-Cattani (YAC) to solve the fractional derivative on Fokker-Plank equation. The HPTM and RPSMs, are used to obtain the solution in terms of Prabhakar function. Numerical examples to extend these ideas and to establish the capability and truthfulness of the proposed method, which makes use of YAC-fractional derivative, is also briefly sketched.

KW - Fokker-Plank equation

KW - HPTM

KW - New fractional derivative

KW - RPSM

KW - Robotnov fractional exponential function

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EP - 1449

JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

IS - 3

ER -

A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator

Abstract

Keywords

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