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Fractional optimal control approach to the diabetics model

Nadeem Muhammad, Habib Mustafa, Arif Ayesha, Asjad Muhammad Imran

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 1

71-82

Diabetes mellitus is one of the most critical diseases, affecting millions of people around the world. This work deals with the fractional optimal control of the dynamics of the population model on diabetes. This framework is based on the fractional order differential problems that describe the population before and after diabetes involving some health problems. We consider the Caputo derivatives for the study of the proposed model. The maximum principle of Pontryagin is utilized to derive the necessary conditions for the optimality of a dynamical system. Using a forward-backward sweep approach with the generalized Euler method accomplishes numerical solutions of formulated issues.

The effect of basalt knitted fabric on the properties of green epoxy resin

Jamshaid Hafsa, Rajput Abdul Waqar, Zahid Bilal, Memon Sanam, Qureshi Raja Fahad, Aslam Sarmad, Nadeem Muhammad

Polimery

2022

Vol. 67, nr 2

67--71

The influence of basalt fabric on the tensile mechanical properties and the impact resistance of green epoxy resin was investigated. Composites with parallel arrangement of insert yarns had better properties than in the case of their perpendicular arrangement. The properties were also influenced by the number of layers of the fabric. The tensile strength and impact resistance of the composites were better than the commercially available side mirror covers due to the superior properties of the basalt fiber.

Zbadano wpływ tkaniny bazaltowej na właściwości mechaniczne przy rozciąganiu i odporność na uderzenie „zielonej” żywicy epoksydowej. Kompozyty o równoległym ułożeniu przędzy charakteryzowały się lepszymi właściwościami niż te o prostopadłym ułożeniu. Na właściwości miała również wpływ liczba warstw tkaniny. Wytrzymałość na rozciąganie i odporność na uderzenie kompozytów były lepsze niż dostępnych na rynku osłon lusterek bocznych ze względu na dobre właściwości włókna bazaltowego.

Investigation of the settlement prediction in soft soil by Richards Model: based on a linear least squares-iteration method

Nadeem Muhammad, Akbar Muhammad, Huali Pan, Xiaoqing Li, Guoqiang Ou, Amin Azka

Archives of Civil Engineering

2021

Vol. 67, nr 2

491--506

Prediction of soft soil sub-grades settlement has been a big challenge for geotechnical engineers that are responsible for the design of roadbed embankment. The characteristics of low strength, poor permeability, high water contents, and high compressibility are dominant in soft soils, which result in a huge settlement in the case of long-term loading. The settlement prediction in soft soil subgrades of Jiehui Expressway A1, Guangdong, China, is the focus of this study. For this purpose, the necessary data of settlement is collected throughout the project execution. The numerical analysis is conducted by using the Richards model based on Linear Least Squares Iteration (LLS-I) method to calculate and predict the expected settlement. The traditional settlement prediction methods, including the hyperbolic method, exponential curve method, and pearl curve method, are applied on field settlement data of soft soil subgrades of Jiehui Expressway A1. The results show that the Richards model based on Linear Least Squares Iteration (LLS-I) method has high precision, and it has proven to be a better option for settlement prediction of soft soil sub-grades. The model analysis indicates that the mean absolute percentage error (MAPE) can be minimized as compared to other soft soil sub-grades settlement prediction methods. Hence, Richards's model-based LLS-I method has a capability for simulation and settlement prediction of soft soil subgrades.