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    Error Bounds for Fractional Integral Inequalities with Applications
    (Mdpi, 2024) Alqahtani, Nouf Abdulrahman; Qaisar, Shahid; Munir, Arslan; Naeem, Muhammad; Budak, Huseyin
    Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite-Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo-Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite-Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.
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    Identification of phytotoxins in different plant parts of Brassica napus and their influence on mung bean
    (Springer Heidelberg, 2018) Mehmood, Azhar; Naeem, Muhammad; Khalid, Farhan; Saeed, Yousaf; Abbas, Tasawer; Jabran, Khawar; Javaid, Muhammad Mansoor
    Plants in Brassica genus have been found to possess strong allelopathic potential. They may inhibit seed germination and emergence of subsequent crops following them in a rotation system. Series of laboratory and greenhouse experiments were conducted to determine the allelopathic impacts of Brassica napus L. against mung bean. We studied (1) the effects of aqueous extract (5%) of different plant parts (root, stem, leaf, flower, and whole plant) of B. napus, (2) the effects of leaf and flower extracts of B. napus at 0, 1, 2, 3, and 4% concentrations, and (3) the effect of residues of different B. napus plant parts and decomposition periods (0, 7, 14, and 21 days) on germination and seedling growth of mung bean. Various types of phenolics including quercitin, chlorogenic acid, p-coumeric acid, m-coumaric acid, benzoic acid, caffeic acid, syringic acid, vanillic acid, ferulic acid, cinamic acid, and gallic acid were identified in plant parts of B. napus. Among aqueous extracts of various plant parts, leaf and flower were found to have stronger inhibitory effects on germination and seedling growth traits of mung bean, higher concentrations were more toxic. The decomposition period changed the phtotoxic effect of residues, more inhibitory effect was shown at 14 days decomposition while decomposition for 21 days reduced inhibitory effect. The more total water-soluble phenolic was found in 5% (w/v) aqueous extract and 5% (w/w) residues of B. napus flowers at 14 days of decomposition (89.80 and 10.47 mg L-1), respectively. The strong inhibitory effects of B. napus should be managed when followed in rotation.