Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals
Küçük Resim Yok
Tarih
2025
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Milne's inequality provides an upper bound for the error in definite integral approximations using Milne's rule, making it a useful tool for evaluating the rule's precision. For this reason, this inequality is widely applied in engineering, physics, and applied mathematics. Additionally, conformable fractional integral operators establish a stronger relationship between classical and fractional calculus, enhancing the modeling, analysis, and resolution of complex problems. Therefore, we focus on the study of conformable fractional integral operators and Milne-type inequalities, which have significant applications in various fields. In this study, we first obtain an integral identity involving conformable fractional integral operators and twice-differentiable functions. Building on this new identity, we develop various perturbed Milne-type integral inequalities for twice-differentiable convex functions. We also validate them numerically through examples, computational analysis, and visual representations. In conclusion, it is evident that our findings significantly enhance and expand upon prior findings regarding integral inequalities. In addition to improving the scope of previous discoveries, the obtained results offer meaningful approaches and methods for tackling mathematical and scientific issues.
Açıklama
Anahtar Kelimeler
Milne-type integral inequalities, Convex functions, Riemann-Liouville fractional integrals, Conformable fractional integrals
Kaynak
Boundary Value Problems
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
2025
Sayı
1
