Some trapezoid and midpoint type inequalities via fractional (p,q)-calculus

Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q -calculus has been investigated and applied in a variety of research subjects including the fractional q -trapezoid and q -midpoint type inequalities. Fr...

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Published inAdvances in difference equations Vol. 2021; no. 1; pp. 1 - 22
Main Authors Neang, Pheak, Nonlaopon, Kamsing, Tariboon, Jessada, Ntouyas, Sotiris K., Agarwal, Praveen
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 13.07.2021
Springer Nature B.V
SpringerOpen
Subjects
( p , q ) $(p,q)$ -calculus
Analysis
Calculus
Continuity (mathematics)
Difference and Functional Equations
Fractional ( p , q ) $(p,q)$ -integral
Fractional calculus
Functional Analysis
Identities
Inequalities
Integrals
Intervals
Mathematical analysis
Mathematics
Mathematics and Statistics
Midpoint type inequalities
Ordinary Differential Equations
Partial Differential Equations
q-shifting operator
Quantum calculus
Trapezoid type inequalities
Midpoint type inequalities
05A30
26D10
shifting operator
integral
26A33
Fractional
integral inequalities
Trapezoid type inequalities
calculus
Quantum calculus
26D15
Online AccessGet full text
ISSN1687-1847
1687-1839
1687-1847
DOI10.1186/s13662-021-03487-6

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Abstract Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q -calculus has been investigated and applied in a variety of research subjects including the fractional q -trapezoid and q -midpoint type inequalities. Fractional ( p , q ) -calculus on finite intervals, particularly the fractional ( p , q ) -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional ( p , q ) -integral on finite intervals. Then, the obtained results are used to derive some fractional ( p , q ) -trapezoid and ( p , q ) -midpoint type inequalities.
AbstractList Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q -calculus has been investigated and applied in a variety of research subjects including the fractional q -trapezoid and q -midpoint type inequalities. Fractional ( p , q ) -calculus on finite intervals, particularly the fractional ( p , q ) -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional ( p , q ) -integral on finite intervals. Then, the obtained results are used to derive some fractional ( p , q ) -trapezoid and ( p , q ) -midpoint type inequalities.
Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional (p,q)-calculus on finite intervals, particularly the fractional (p,q)-integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional (p,q)-integral on finite intervals. Then, the obtained results are used to derive some fractional (p,q)-trapezoid and (p,q)-midpoint type inequalities.
Abstract Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional ( p , q ) $(p,q)$ -calculus on finite intervals, particularly the fractional ( p , q ) $(p,q)$ -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional ( p , q ) $(p,q)$ -integral on finite intervals. Then, the obtained results are used to derive some fractional ( p , q ) $(p,q)$ -trapezoid and ( p , q ) $(p,q)$ -midpoint type inequalities.
Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q -calculus has been investigated and applied in a variety of research subjects including the fractional q -trapezoid and q -midpoint type inequalities. Fractional $(p,q)$ ( p , q ) -calculus on finite intervals, particularly the fractional $(p,q)$ ( p , q ) -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional $(p,q)$ ( p , q ) -integral on finite intervals. Then, the obtained results are used to derive some fractional $(p,q)$ ( p , q ) -trapezoid and $(p,q)$ ( p , q ) -midpoint type inequalities.
ArticleNumber 333
Author Tariboon, Jessada
Nonlaopon, Kamsing
Neang, Pheak
Agarwal, Praveen
Ntouyas, Sotiris K.
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  orcidid: 0000-0001-7556-8942
  surname: Agarwal
  fullname: Agarwal, Praveen
  organization: International Center for Basic and Applied Sciences, Department of Mathematics, Anand International College of Engineering
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Copyright_xml – notice: The Author(s) 2021
– notice: The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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Issue 1
Keywords Midpoint type inequalities
05A30
26D10
shifting operator
integral
26A33
Fractional
integral inequalities
Trapezoid type inequalities
calculus
Quantum calculus
26D15
Language English
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Snippet Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q -calculus...
Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has...
Abstract Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional...
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SubjectTerms ( p , q ) $(p,q)$ -calculus
Analysis
Calculus
Continuity (mathematics)
Difference and Functional Equations
Fractional ( p , q ) $(p,q)$ -integral
Fractional calculus
Functional Analysis
Identities
Inequalities
Integrals
Intervals
Mathematical analysis
Mathematics
Mathematics and Statistics
Midpoint type inequalities
Ordinary Differential Equations
Partial Differential Equations
q-shifting operator
Quantum calculus
Trapezoid type inequalities
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Title Some trapezoid and midpoint type inequalities via fractional (p,q)-calculus
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