New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Rashid, Saima; Khalid, Aasma; Bazighifan, Omar; Oros, Georgia Irina

doi:10.3390/math9151753

Open AccessArticle

New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

¹

Department of Mathematics, Government College University, Faisalabad 38000, Pakistan

²

Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan

³

Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

⁴

Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen

⁵

Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2021, 9(15), 1753; https://doi.org/10.3390/math9151753

Submission received: 17 June 2021 / Revised: 21 July 2021 / Accepted: 22 July 2021 / Published: 26 July 2021

(This article belongs to the Special Issue Analytic and Geometric Inequalities: Theory and Applications)

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Abstract

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

Keywords: Hermite–Hadamard inequality; Ostrowski type inequality; ℘-convex function; generalised fractional integral; matrices; Fox–Wright function

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MDPI and ACS Style

Rashid, S.; Khalid, A.; Bazighifan, O.; Oros, G.I. New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications. Mathematics 2021, 9, 1753. https://doi.org/10.3390/math9151753

AMA Style

Rashid S, Khalid A, Bazighifan O, Oros GI. New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications. Mathematics. 2021; 9(15):1753. https://doi.org/10.3390/math9151753

Chicago/Turabian Style

Rashid, Saima, Aasma Khalid, Omar Bazighifan, and Georgia Irina Oros. 2021. "New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications" Mathematics 9, no. 15: 1753. https://doi.org/10.3390/math9151753

APA Style

Rashid, S., Khalid, A., Bazighifan, O., & Oros, G. I. (2021). New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications. Mathematics, 9(15), 1753. https://doi.org/10.3390/math9151753

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

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