New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite-Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems.
Açıklama
Anahtar Kelimeler
Hermite-Hadamard-type inequalities, Midpoint-type inequalities, Convex functions, Proportional Caputo-hybrid operator, Differentiable Mappings, Fractional Derivatives, Real Numbers
Kaynak
Journal of Inequalities And Applications
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
2024
Sayı
1
