Yazar "Barakat, Mohamed A." seçeneğine göre listele
Listeleniyor 1 - 4 / 4
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe Fractional Milne-type inequalities for twice differentiable functions(Amer Inst Mathematical Sciences-Aims, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, Hüseyin; Barakat, Mohamed A.In this study, a specific identity was derived for functions that possess two continuous derivatives. Through the utilization of this identity and Riemann-Liouville fractional integrals, several fractional Milne-type inequalities were established for functions whose second derivatives inside the absolute value are convex. Additionally, an example and a graphical representation are included to clarify the core findings of our research.Öğe Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions(Amer Inst Mathematical Sciences-Aims, 2024) Hyder, Abd-Allah; Budak, Hüseyin; Barakat, Mohamed A.This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.Öğe New Versions of Midpoint Inequalities Based on Extended Riemann-Liouville Fractional Integrals(Mdpi, 2023) Hyder, Abd-Allah; Budak, Hueseyin; Barakat, Mohamed A.This study aims to prove some midpoint-type inequalities for fractional extended Riemann-Liouville integrals. Crucial equality is proven to build new results. Using this equality, several midpoint-type inequalities are established via differentiable convex functions and the proposed extended fractional operators. To be more specific, the well-known Holder, Jensen, and power mean integral inequalities are employed in the demonstrated inequalities. Additionally, many remarks based on specific selections of the main results are presented. Moreover, to illustrate the key conclusions, a few instances are provided.Öğe On New Fractional Version of Generalized Hermite-Hadamard Inequalities(Mdpi, 2022) Hyder, Abd-Allah; Almoneef, Areej A.; Budak, Hüseyin; Barakat, Mohamed A.In this study, we establish a novel version of Hermite-Hadamard inequalities through neoteric generalized Riemann-Liouville fractional integrals (RLFIs). For functions with the convex absolute values of derivatives, we create a variety of midpoint and trapezoid form inequalities, including the generalized RLFIs. Moreover, multiple fractional inequalities can be produced as special cases of the findings of this study.
