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Peer-reviewedCC BY 4.0Fractal and Fractional

Bullen–Simpson-Type Inequalities for Fractal-Fractional Integrals Involving Generalized Harmonic Convex Functions

  • Bandar Bin-Mohsin1
  1. 1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Abstract

This article is devoted to the derivation of new inequalities within the theory of fractal–fractional calculus. Its principal contribution is the construction of a new auxiliary identity of fractal–fractional type. By exploiting this identity, we establish a variety of Bullen–Simpson-type inequalities associated with functions whose local fractional derivatives possess generalized harmonic convexity. Moreover, by employing the generalized Hölder and power mean inequalities, we derive supplementary bounds that further enhance the scope of the analysis. The accuracy of the theoretical developments is illustrated through a representative example, together with graphical visualizations that substantiate the consistency of the proposed results. Finally, an application to certain special fractal means is presented in order to demonstrate the effectiveness and practical relevance of the obtained inequalities.

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Cite

BibTeXRIS
BibTeX
@article{binmohsin2026bullensimpsontype,
  title = {{Bullen–Simpson-Type Inequalities for Fractal-Fractional Integrals Involving Generalized Harmonic Convex Functions}},
  author = {Bandar Bin-Mohsin},
  journal = {Fractal and Fractional},
  year = {2026},
  month = nov,
  doi = {10.3390/fractalfract10110777},
  url = {https://www.mdpi.com/2504-3110/10/11/777},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Bullen–Simpson-Type Inequalities for Fractal-Fractional Integrals Involving Generalized Harmonic Convex Functions
AU  - Bandar Bin-Mohsin
PY  - 2026
DA  - 2026/11/07
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10110777
UR  - https://www.mdpi.com/2504-3110/10/11/777
AB  - This article is devoted to the derivation of new inequalities within the theory of fractal–fractional calculus. Its principal contribution is the construction of a new auxiliary identity of fractal–fractional type. By exploiting this identity, we establish a variety of Bullen–Simpson-type inequalities associated with functions whose local fractional derivatives possess generalized harmonic convexity. Moreover, by employing the generalized Hölder and power mean inequalities, we derive supplementary bounds that further enhance the scope of the analysis. The accuracy of the theoretical developments is illustrated through a representative example, together with graphical visualizations that substantiate the consistency of the proposed results. Finally, an application to certain special fractal means is presented in order to demonstrate the effectiveness and practical relevance of the obtained inequalities.
SN  - 2504-3110
ER  -