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Peer-reviewedCC BYInternational Journal of Analysis and Applications

Some New Notions of Mathematical Integral Inequalities: Theory and Applications

  • Hijaz Ahmad
  • Muhammad Usman Tariq1,2
  • Ali Asghar3
  • Waqar Afzal4,5
  • Maggie Aphane6,7
  • Rakib Efendiev8
8 affiliations
  1. 1Department of Mathematics , Capt Waqar Kakar Shaheed Balochistan Residential College , Loralai , 84800 , Balochistan , Pakistan
  2. 2Mathematics Research Center , Near East University , Near East Boulevard , PC: 99138 , Nicosia / Mersin 10 , Turkey
  3. 3Department of Basic Sciences and Related Studies , Mehran UET , Jamshoro , Sindh , Pakistan
  4. 4Abdus Salam School of Mathematical Sciences , GC University , Lahore 54600 , Pakistan
  5. 5Center for Theoretical Physics , Khazar University , 41 Mehseti Str. , Baku , AZ1096 , Azerbaijan
  6. 6National Institute for Theoretical and Computational Sciences (NITheCS) , South Africa
  7. 7Sefako Makgatho Health Sciences University , Garankuwa , Medusa , 0204 , South Africa
  8. 8Baku Engineering University , Scientific Research Centre , H.Aliyev , 120 , Baku , AZ0101 , Azerbaijan
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Abstract

Convex analysis and mathematical inequalities play a fundamental role in both pure and applied sciences. In this work, we first explore the notion of n-fractional polynomial s-like m-convexity involving Raina’s mapping and also its algebraic properties. We then introduce a novel Hermite–Hadamard (H-H), midpoint H-H, trapezoid H-H type inequalities based on this generalized concept and the k-fractional operator. Several related corollaries and examples are examined, particularly in connection with the Mittag–Leffler function. The practical utility of the proposed inequalities is demonstrated through applications to viscoelastic materials with fractional damping, supported by computational algorithms, and a numerical example involving fractional diffusion in fractured media. The results provide meaningful refinements and novel insights that extend and enrich existing research in the field.

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Cite

BibTeXRIS
BibTeX
@article{ahmad2026some,
  title = {{Some New Notions of Mathematical Integral Inequalities: Theory and Applications}},
  author = {Hijaz Ahmad and Muhammad Usman Tariq and Ali Asghar and Waqar Afzal and Maggie Aphane and Rakib Efendiev},
  journal = {International Journal of Analysis and Applications},
  year = {2026},
  month = may,
  doi = {10.28924/2291-8639-24-2026-175},
  url = {https://doi.org/10.28924/2291-8639-24-2026-175},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Some New Notions of Mathematical Integral Inequalities: Theory and Applications
AU  - Hijaz Ahmad
AU  - Muhammad Usman Tariq
AU  - Ali Asghar
AU  - Waqar Afzal
AU  - Maggie Aphane
AU  - Rakib Efendiev
PY  - 2026
DA  - 2026/05/29
JO  - International Journal of Analysis and Applications
DO  - 10.28924/2291-8639-24-2026-175
UR  - https://doi.org/10.28924/2291-8639-24-2026-175
AB  - Convex analysis and mathematical inequalities play a fundamental role in both pure and applied sciences. In this work, we first explore the notion of n-fractional polynomial s-like m-convexity involving Raina’s mapping and also its algebraic properties. We then introduce a novel Hermite–Hadamard (H-H), midpoint H-H, trapezoid H-H type inequalities based on this generalized concept and the k-fractional operator. Several related corollaries and examples are examined, particularly in connection with the Mittag–Leffler function. The practical utility of the proposed inequalities is demonstrated through applications to viscoelastic materials with fractional damping, supported by computational algorithms, and a numerical example involving fractional diffusion in fractured media. The results provide meaningful refinements and novel insights that extend and enrich existing research in the field.
SN  - 2291-8639
ER  -