A New Dynamic Scheme via Fractional Operators on Time Scale

Saima Rashid; Muhammad Aslam Noor; Kottakkaran Sooppy Nisar; Dumitru Baleanu; Gauhar Rahman

doi:10.3389/fphy.2020.00165

A New Dynamic Scheme via Fractional Operators on Time Scale

Saima Rashid
, Muhammad Aslam Noor
, Kottakkaran Sooppy Nisar
, Dumitru Baleanu
, Gauhar Rahman

Mathematics

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

19 Scopus citations

Abstract

The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Grüss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.

Original language	English
Article number	165
Journal	Frontiers in Physics
Volume	8
DOIs	https://doi.org/10.3389/fphy.2020.00165
State	Published - 3 Jun 2020

Keywords

fractional calculus
generalized riemann-liouville fractional integral operator
gruss inequality
holder inequality
Minkowski' inequlity
rimenn-liouville fractional integral operator
time sccale

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10.3389/fphy.2020.00165

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title = "A New Dynamic Scheme via Fractional Operators on Time Scale",

abstract = "The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Gr{\"u}ss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.",

keywords = "fractional calculus, generalized riemann-liouville fractional integral operator, gruss inequality, holder inequality, Minkowski' inequlity, rimenn-liouville fractional integral operator, time sccale",

author = "Saima Rashid and \{Aslam Noor\}, Muhammad and Nisar, \{Kottakkaran Sooppy\} and Dumitru Baleanu and Gauhar Rahman",

note = "Publisher Copyright: {\textcopyright} Copyright {\textcopyright} 2020 Rashid, Aslam Noor, Nisar, Baleanu and Rahman.",

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doi = "10.3389/fphy.2020.00165",

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AU - Rashid, Saima

AU - Aslam Noor, Muhammad

AU - Nisar, Kottakkaran Sooppy

AU - Baleanu, Dumitru

AU - Rahman, Gauhar

PY - 2020/6/3

Y1 - 2020/6/3

N2 - The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Grüss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.

AB - The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Grüss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.

KW - fractional calculus

KW - generalized riemann-liouville fractional integral operator

KW - gruss inequality

KW - holder inequality

KW - Minkowski' inequlity

KW - rimenn-liouville fractional integral operator

KW - time sccale

UR - https://www.scopus.com/pages/publications/85086792152

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DO - 10.3389/fphy.2020.00165

M3 - Article

AN - SCOPUS:85086792152

SN - 2296-424X

VL - 8

JO - Frontiers in Physics

JF - Frontiers in Physics

M1 - 165

ER -

A New Dynamic Scheme via Fractional Operators on Time Scale

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Keywords

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