Some Novel Error Bounds of Boole's Formula-Type Inequalities in Quantum Calculus With Computational Analysis and Applications

Hussain M., Mateen A., Aslam S., BUDAK H.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/mma.70275
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Boole's formula-type inequalities, convex function, error bounds, Mittag-Leffler function, quadrature formulas, quantum calculus
  • Kocaeli Üniversitesi Adresli: Evet

Özet

Quantum calculus extends classical calculus through the inclusion of a parameter (Formula presented.), thereby broadening the conceptual framework for analysis. The present study provides novel variants of Boole's formula-type inequalities for (Formula presented.) -differentiable convex functions via first deriving an essential quantum-integral identity. The derived results enhance classical findings and highlight the distinctive properties of convex functions in quantum calculus. The application to quadrature formula, special means of real numbers, and the Mittag-Leffler function demonstrates the practical relevance of our newly derived results. Numerical and graphical examples further verify the accuracy and effectiveness of the presented inequalities, indicating their suitability for real-world circumstances. The present work strengthens the theoretical understanding of Boole's formula-type inequalities in quantum and classical domains and offers interesting possibilities for future research in numerical analysis.