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This paper presents a method for trajectory tracking of constrained mobile manipulators under both holonomic and nonholonomic constraints. An adaptive robust motion/force controller with a Radial Basis Function (RBF) neural network is proposed to improve the tracking control based on the dynamic model with external disturbances and parameter uncertainties. In this proposed control strategy, the model-based robust compensator is associated with an adaptive controller, which is based on model-free RBF network; it can effectively enhance the control performance. With the proposed method, the trajectory and constraint force can be converged asymptotically to their respective values to reach the desired levels. Neural network estimation errors, as well as boundedness on parameter uncertainties, are all strictly controlled by an updated law of adaptive control. Lyapunov stability theory and the stability of a closed-loop system are ensured by the adaptive robust controller. Finally, simulation results of the proposed approach in a comparative manner with model-based and model-free controllers are performed to demonstrate the adequate performance of adaptive robust control in tracking errors and have a faster reduction rate.

The aim of this paper is to present a new numerical scheme, namely the fractional multi-delay block boundary value method (FMDBBVM), which is proposed to solve fractional differential equations (FDEs) with multiple delays. The FMDBBVM is proposed via a combination of the block boundary value method (BBVM) and the Lagrange interpolating polynomial. In the methodology of the FMDBBVM, the fractional derivative is approximated through a qth-order Lagrange interpolating polynomial with mth-order BBVM. The largest delay is dealt with a modification in the BBVM, and the remaining delays are approximated in the mesh concerning to the largest delay via the Lagrange interpolating polynomial of (w1+w2+1)thorder. The proposed scheme is theoretically showed to be globally stable and convergent with order min{m,q-α+1,w1+w2+1}. Further, a reduced scheme is obtained corresponding to the FMDBBVM for the fractional delay differential equations (FDDEs) in which multiple delays can be accommodated in a single mesh. This scheme is also convergent with order min{m,q-α+1}, and it is also globally stable. The numerical efficiency of both the proposed schemes is demonstrated with the help of some examples.

The continuing coronavirus pandemic has come up with considerable questions in front of the world. Presently, India is among concerned countries in Asia. Even though the recovery rate is more than the death rate, it is affecting human lives and experiencing losses to the market. Several methods were employed to study the spread of novel coronavirus. Mathematical modeling is one of the prominent techniques to evaluate the dynamics of novel coronavirus. In this work, we extend the mathematical model SEIAQRDT by incorporating environmental transmission to analyze the transmission of coronavirus in India. The notable aspect of the model incorporates asymptomatic population, quarantine individuals, and environmental transmission factors. These factors have enormous significance in the ongoing COVID-19 outbreak. The basic reproduction number R0is calculated theoretically. Bifurcation analysis of R0is also done analytically. The existence and stability analysis of disease-free equilibrium (DFE) and endemic equilibrium (EE) points are established. The impact of environmental factors in spreading COVID-19 pandemic is deliberated. The case study for India and Italy is presented and compared with real data, and the results are in accordance with the real situation.

Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis.

Mathematical modeling plays a crucial role in disease modeling. Therefore, in this work, a mathematical model for novel coronavirus is proposed using Caputo-Fabrizio (CF) fractional derivative, while considering the issue of dimensional mismatch for proposed model. This model consists of paramount compartments such as asymptomatic and quarantined. Subsequently, existence and uniqueness of proposed model are shown with the help of fixed-point theorem. The boundedness of solutions is also established using Laplace transform. The local and global stability of disease-free equilibrium point (DFE) of the proposed fractional order model is evaluated. The model is numerically solved using the three-point Adams–Bashforth method (ABM). The predicted results are validated through real data for India. For finding the best-fitted parameters which describe the coronavirus scenario, LSQCURVEFIT function in MATLAB is employed. To determine the reliability of the applied technique, we conduct a comparative analysis of ABM method with Euler method. Notably, the results show the efficiency of ABM method. At the same time, sensitivity analysis for parameters in accordance with reproduction number is conferred. Furthermore, numerical results for distinct values of fractional order derivatives are accomplished. This study also shows the long-term trajectories for recovered, active and death cases. The obtained results of the proposed model are in line with real data for fractional order. Additionally, various control measures are also shown graphically. The simulated results show the effectiveness of fractional order derivatives and control parameters which may help government officials and individuals manage the pandemic in a better way.

The coronavirus disease 2019, started spreading around December 2019, still persists in the population all across the globe. Though different countries have been able to cope with the disease to some extent and vaccination for the same has been developed, it cannot be ignored that the disease is still not on the verge of completely eradicating, which in turn creates a need for having deeper insights of the disease in order to understand it well and hence be able to work towards its eradication. Meanwhile, using mitigation strategies like non-pharmaceutical interventions can help in controlling the disease. In this work, our aim is to study the dynamics of COVID-19 using compartmental approach by applying various analytical methods. We obtain formula for important tools like R0and establish the stability of disease-free equilibrium point for R0<1. Further, based on R0, we discuss the stability and existence of the endemic equilibrium point. We incorporate various control strategies possible and using optimal control theory, study their expected positive impacts on the spread of the disease. Later, using a biologically feasible set of parameters, we numerically analyse the model. We even study the trend of the outbreak in China, for over 120 days, where the active cases rise up to a peak and then the curve flattens.