Parametric inequalities involving fractional integrals with exponential kernels

Saleh W., Meftah B., BUDAK H., LAKHDARI A.

Journal of Applied Analysis, 2025 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/jaa-2025-0045
  • Dergi Adı: Journal of Applied Analysis
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, ABI/INFORM, zbMATH
  • Anahtar Kelimeler: Bullen inequality, convex functions, Fractional integrals with exponential kernels, midpoint inequality, Simpson inequality, trapezium inequality
  • Kocaeli Üniversitesi Adresli: Evet

Özet

This paper explores integral inequalities within the framework of fractional integrals having exponential kernels through a parameterized approach. A novel integral identity with a parameter is introduced, forming the basis for deriving a general inequality. From this, several classical inequalities, including midpoint, trapezium, Bullen, Simpson, and corrected Simpson types, are obtained for differentiable convex functions. Numerical examples and graphical analyses are presented to verify the validity of the proposed results. The findings are further demonstrated through applications to special functions, showcasing the versatility of the developed framework.