SavedAdd your journal

Journals / Türk Doğa ve Fen Dergisi / 2026 / Cilt: 15 Sayı: 1

New Fractional Integral Inequalities for Convex and α-Star s-Convex Functions

Sinan Aslan(AGRI IBRAHIM CECEN UNIVERSITY)0000-0001-5970-1926
Ahmet Ocak Akdemir(AGRI IBRAHIM CECEN UNIVERSITY)0000-0003-2466-0508
Pages
50–57
Publication Date
2026-03-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the proof of the integral inequalities obtained, the definition of function classes and basic analysis knowledge are utilized.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, new integral inequalities related to the Caputo-Fabrizio fractional integral operator are obtained using the definitions of convex functions and α-star s- convex function classes.
📊
Key Findings & Data:In the results obtained with α-star s-convex functions, , α^s=1 is taken to obtain special results that have already been added to the literature.
💡
Conclusion & Impact:In the proof of the integral inequalities obtained, the definition of function classes and basic analysis knowledge are utilized.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Convex Function · α-Star s- Convex Function · Caputo-Fabrizio fractional integrals

Abstract

In this study, new integral inequalities related to the Caputo-Fabrizio fractional integral operator are obtained using the definitions of convex functions and α-star s- convex function classes. In the results obtained with α-star s-convex functions, , α^s=1 is taken to obtain special results that have already been added to the literature. The well-known Hölder and Young inequalities for convex functions and α-star s-convex functions are used. In the proof of the integral inequalities obtained, the definition of function classes and basic analysis knowledge are utilized.

🔖

Cite This Article

Aslan, S., Akdemir, A. O. (2026). New Fractional Integral Inequalities for Convex and α-Star s-Convex Functions. Türk Doğa ve Fen Dergisi, Cilt: 15 Sayı: 1, 50–57. https://doi.org/10.46810/tdfd.1585546

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (29)

  1. Pecaric JE, Tong YL. Convex functions, partial orderings, and statistical applications. Academic Press;1992.
  2. Park JK. Hermite - Hadamard - type inequalities for real α-star s−convex mappings. Journal of applied mathematics and informatics. 2010; 28(5_6):1507–1518.
  3. Akdemir AO. Farklı türden konveks fonksiyonlar için koordinatlarda integral eşitsizlikler (Doctoral dissertation, Doktora Tezi, Fen Bilimleri Enstitüsü, Atatürk Üniversitesi, Erzurum), 2012.
  4. Aslan S. Eksponansiyel konveks fonksiyonlar için koordinatlarda integral eşitsizlikler (Doctoral dissertation, PhD thesis, Doktora Tezi, Ağri İbrahim Çeçen Üniversitesi, Lisansüstü Eğitim Enstitüsü), 2023.
  5. Özcan S, İşcan İ. Some new Hermite–Hadamard type inequalities for s-convex function and their applications. Journal of inequalities and applications. 2019; 2019(1): 201.
  6. Set E, Özdemir ME, Sarıkaya MZ, Akdemir AO. Ostrowski-type inequalities for strongly convex functions. Georgian Mathematical Journal. 2018; 25(1): 109-115.
  7. Niculescu C, Persson LE.Convex functions and their applications. New York: Springer. 2006.
  8. Ekinci A, Akdemir AO, Özdemir ME. Integral inequalities for different kinds of convxity via classical inequalities. Turkish Journal of Science. 2020; 5(3): 305-313.
  9. Çakaloğlu MN, Aslan S, Akdemir AO. Hadamard Type Integral Inequalities for Differentiable (h,m)-Convex Functions. Eastern Anatolian Journal of Science. 2021; 7(1): 12-18.
  10. Dragomir SS. Refinements of the Hermite- Hadamard integral inequality for log-convex functions. RGMIA research report collection. 2000; 3(4).
  11. Mehrez K, Agarwal P. New Hermite– Hadamard type integral inequalities for convex functions and their applications. Journal of Computational and Applied Mathematics. 2019; 350: 274-285.
  12. Abdeljawad T, Baleanu D. On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics. 2017; 80(1): 11-27.
  13. Tariq M, Ahmad H, Shaikh AG, Sahoo SK, Khedher KM, Gia TN. New fractional integral inequalities for preinvex functions involving caputo fabrizio operator. AIMS Mathematics. 2022; 7(3): 3440–3455.
  14. Atangana A, Baleanu, D. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. arXiv preprint arXiv. 2016; 1602.03408.
  15. Abdeljawad T, Baleanu D. On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics. 2017; 80(1), 11-27.
  16. Abdeljawad T. On conformable fractional calculus. Journal of computational and Applied Mathematics. 2015; 279, 57-66.
  17. Abdeljawad T, Baleanu D. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. arXiv preprint arXiv. 2016; 1607.00262.
  18. Akdemir, AO., Aslan, S., Çakaloğlu, M. N., Ekinci, A. Some New Results for Different Kinds of Convex Functions Caputo-Fabrizio Fractional Operators. In 4th International Conference on Mathematical and Related Sciences. ICMRS. 2021, p. 92
  19. Akdemir AO, Aslan S, Çakaloğlu MN, Set E. New Hadamard Type Integral Inequalities via Caputo-Fabrizio Fractional Operators. In 4th International Conference on Mathematical and Related Sciences. 2021, p. 91.
  20. Akdemir AO, Aslan S, Ekinci A. Novel Approaches for s-Convex Functions via Caputo-Fabrizio Fractional Integrals. Proceedings of IAM. 2022; 11(1): 3-16.
  21. Akdemir AO, Butt SI, Nadeem M, Ragusa MA. New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics. 2021; 9(2): 122.
  22. Akdemir AO, Ekinci A, Set E. Conformable fractional integrals and related new integral inequalities. Journal of Nonlinear and Convex Analysis 2017; 18(4): 661-674.
  23. Gürbüz M, Akdemir AO, Rashid S, Set E. Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities. Journal of Inequalities and Applications. 2020, p. 1-10.
  24. Aslan S. Some Novel Fractional Integral Inequalities for Different Kinds of Convex Functions. Eastern Anatolian Journal of Science. 2023; 9(1): 27-32.
  25. Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation Applications. 2015; 1(2): 73-85.
  26. Al-Smadi M, Dutta H, Hasan S, Momani S. On numerical approximation of Atangana-aleanu-Caputo fractional integro-differential euations under uncertainty in Hilbert Space. Mathematical Modelling of Natural Phenomena. 2021; 16:41.
  27. Al-Smadi M, Djeddi N, Momani S, Al-Omari S, Araci S. An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space. Advances in Difference Equations. 2021; (1): 271.
  28. Momani S, Djeddi N, Al-Smadi M, Al-Omari S. Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method. Applied Numerical Mathematics. 2021; 170: 418-434.
  29. Sene N. Stability analysis of the fractional differential equations with the Caputo-Fabrizio fractional derivative. Journal of Fractional Calculus and Applications. 2020; 11(2): 160-172.