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

Author

Listed:
  • Saima Rashid

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
    These authors contributed equally to this work.)

  • Aasma Khalid

    (Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan
    These authors contributed equally to this work.)

  • Omar Bazighifan

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
    Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
    These authors contributed equally to this work.)

  • Georgia Irina Oros

    (Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Saima Rashid & Aasma Khalid & Omar Bazighifan & Georgia Irina Oros, 2021. "New Modifications of Integral Inequalities via ℘ -Convexity Pertaining to Fractional Calculus and Their Applications," Mathematics, MDPI, vol. 9(15), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1753-:d:601321
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    References listed on IDEAS

    as
    1. Saima Rashid & Rehana Ashraf & Kottakkaran Sooppy Nisar & Thabet Abdeljawad & Imtiaz Ahmad, 2020. "Estimation of Integral Inequalities Using the Generalized Fractional Derivative Operator in the Hilfer Sense," Journal of Mathematics, Hindawi, vol. 2020, pages 1-15, October.
    2. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    3. Rashid, Saima & Sultana, Sobia & Hammouch, Zakia & Jarad, Fahd & Hamed, Y.S., 2021. "Novel aspects of discrete dynamical type inequalities within fractional operators having generalized ℏ-discrete Mittag-Leffler kernels and application," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
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