Numerical Approximations and Fractional Calculus: Extending Boole's Rule with Riemann-LiouvilleFractional Integral Inequalities
Küçük Resim Yok
Tarih
2025
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann-Liouville fractional integrals is established, forming the foundation for deriving novel fractional Boole-type inequalities tailored to differentiable convex functions. The proposed framework encompasses a wide range of functional classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation, thereby broadening the applicability of these inequalities to diverse mathematical settings. The research emphasizes the importance of the Riemann-Liouville fractional operator in solving problems related to non-integer-order differentiation, highlighting its pivotal role in enhancing classical inequalities. These newly established inequalities offer sharper error bounds for various numerical quadrature formulas in classical calculus, marking a significant advancement in computational mathematics. Numerical examples, computational analysis, applications to quadrature formulas and graphical illustrations substantiate the efficacy of the proposed inequalities in improving the accuracy of integral approximations, particularly within the context of fractional calculus. Future directions for this research include extending the framework to incorporate q-calculus, symmetrized q-calculus, alternative fractional operators, multiplicative calculus, and multidimensional spaces. These extensions would enable a comprehensive exploration of Boole's formula and its associated error bounds, providing deeper insights into its performance across a broader range of mathematical and computational settings.
Açıklama
Anahtar Kelimeler
inequalities of Boole's type, fractional calculus, quadrature formulas, Riemann-Liouville fractional integrals, error bounds, functions with convexity, Lipschitz continuity, boundedness
Kaynak
Fractaland Fractional
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
9
Sayı
1
