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Start Over Author "Khaliq, Abdul" Publication Type Academic Journals
676 results on '"Khaliq, Abdul"'

38. Rational Approximations for the Oscillatory Two-Parameter Mittag–Leffler Function.

Author

Honain, Aljowhara H., Furati, Khaled M., Sarumi, Ibrahim O., and Khaliq, Abdul Q. M.

Abstract

The two-parameter Mittag–Leffler function E α , β is of fundamental importance in fractional calculus, and it appears frequently in the solutions of fractional differential and integral equations. However, the expense of calculating this function often prompts efforts to devise accurate approximations that are more cost-effective. When α > 1 , the monotonicity property is largely lost, resulting in the emergence of roots and oscillations. As a result, current rational approximants constructed mainly for α ∈ (0 , 1) often fail to capture this oscillatory behavior. In this paper, we develop computationally efficient rational approximants for E α , β (− t) , t ≥ 0 , with α ∈ (1 , 2) . This process involves decomposing the Mittag–Leffler function with real roots into a weighted root-free Mittag–Leffler function and a polynomial. This provides approximants valid over extended intervals. These approximants are then extended to the matrix Mittag–Leffler function, and different implementation strategies are discussed, including using partial fraction decomposition. Numerical experiments are conducted to illustrate the performance of the proposed approximants. [ABSTRACT FROM AUTHOR]

Published
2024
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39. Iron–Carbon Nanospheres as Promising Material for Magnetic Assisted Adsorption and Separation of Impurities from a Liquid Phase.

Author

Pełech, Iwona, Lewinska, Sabina, Arciszewska, Monika, Khaliq, Abdul, Ślawska-Waniewska, Anna, Sibera, Daniel, Staciwa, Piotr, and Narkiewicz, Urszula

Subjects
MAGNETIC materials, CEMENTITE, MAGNETIC properties, IRON compounds, MAGNETIC separation, MAGNETITE, ADSORPTION (Chemistry)
Abstract

The composites containing various iron compounds and highly microporous carbon spheres were produced and investigated for structural and magnetic properties. Iron citrate, nitrate and chloride were used to prepare samples and the obtained products contained iron, iron carbide or magnetite. All the produced samples were characterized by high porosity and good magnetic properties. The coupling of the high porosity of carbon spheres with magnetic properties of iron compounds provides a potential application of the composites to removal of impurities from water, followed by a magnetic separation of the sorbent. [ABSTRACT FROM AUTHOR]

Published
2024
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40. Mitigating the Toxic Effects of Salinity in Wheat through Exogenous Application of Moringa Leaf Extract.

Author

Muneeba, Khaliq, Abdul, Muhammad, Faran, Khan, Muhammad Dilawaz, Alharbi, Sulaiman Ali, Ansari, Mohammad Javed, Umer, Muhammad, Aslam, Muhammad Talha, and Shahzad, Haroon

Subjects
POISONS, MORINGA, SALINITY, PHOTOSYNTHETIC pigments, HYDROGEN peroxide, CULTIVARS, WHEAT
Abstract

Allelochemicals have emerged as an important player in inducing the abiotic stress tolerance. The experiment included three components: different levels of salinity stress (SS: control, 6 dS m-1, 12 dS m-1), seed priming with moringa leaf extract (MLE: 0.5%, 1.0%, 1.5%, 2.0%, 2.5%, 3.0%), and saltwater-tolerant and salinity-sensitive wheat cultivars (Faisalabad-2008, Galaxy-2013). Results showed that salinity lowered photosynthetic pigments, photosynthesis, transpiration, internal carbon, and stomatal conductance while causing poor and delayed germination, inconsistent seedling growth, and increased hydrogen peroxide accumulation. However, hydro-priming and MLE priming enhanced emergence dynamics, growth, biochemical and enzymatic characteristics, and physiological aspects. The cultivar Faisalabad-2008 (wheat) performed well, but at high salinity levels, the hormetic impact of moringa leaf extract was more obvious, enhancing the germination and growth of cultivar Galaxy-2013, which was salinity-sensitive. Wheat cultivars' germination and seedling growth improved most when primed with 2% MLE (Faisalabad-2008) and 2.5% MLE (Galaxy-2013). This demonstrated that moringa possesses growthpromoting compounds that efficiently mitigate the toxic impacts of salinity. [ABSTRACT FROM AUTHOR]

Published
2024
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