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Ghulam Farid,Sidra Bibi,Laxmi Rathour,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 강원경기수학회 2023 한국수학논문집 Vol.31 No.1
We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly $(s,m)$-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.
Abdul Haleem,Sidra Bibi Syaal,Muhammad Ajmal,Jaweria Ambreen,Sajid Rauf,Nasir Ali,Saz Muhammad,Afzal Shah,Muhammad Abid Zia,Muhammad Siddiq 한국화학공학회 2020 Korean Journal of Chemical Engineering Vol.37 No.4
Here in, we demonstrate facile fabrication of silver and palladium nanoparticles in dual responsive poly(Nisopropylacrylamide- co-2-Acrylamido-2-methylpropane sulfonic acid) microgel with temperature- and pH-dependent catalytic potential. Palladium-based catalyst showed better catalytic efficiency as compared to silver-based catalyst for degradation of Rhodamine-B and P-Nitrophenol in aqueous medium under the same set of reaction conditions. The responsive nature of the microgel was found to be useful to tune the catalytic activity of the as-prepared catalysts, and reduction rate was enhanced with the pH and temperature elevation of the reaction medium; however, the increasing trend was slowed in the volume phase transition region of the microgel. Under a specific set of reaction conditions, the reduction of Rhodamine-B was as fast as 0.968 and 0.571 min1 when catalyzed with palladium and silver based catalysts, respectively. The hydrodynamic radius of the particles of microgel support was found to be in the range of 65- 180 nm when pH and temperature of the medium were varied in the range of 2-12 and 25-45, respectively. The estimated diameter of silver and palladium nanoparticles fabricated in the microgel support under the same set of reaction conditions was 9-15 and 7-11 nm, respectively.
GHULAM FARID,LAXMI RATHOUR,SIDRA BIBI,MUHAMMAD SAEED AKRAM,LAKSHMI NARAYAN MISHRA,VISHNU NARAYAN MISHRA The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined (α,h-m)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function h is bounded above by ${\frac{1}{\sqrt{2}}}$.
Ghulam Farid,Laxmi Rathour,Muhammad Saeed Akram,Sidra Bibi,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined ($\alpha$,$h$-$m$)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function $h$ is bounded above by $\frac{1}{\sqrt{2}}$.