Mathematics and Computational Sciences
Volume:3 Issue: 3, Summer 2022

In the present article‎, ‎to find the answer to the mobile-immobile advection-dispersion model of temporal fractional order $0< \beta \leq 1$ (MI-ADM-TF)‎, ‎which can be applied to model the solute forwarding in watershed catchment and flood‎, ‎the effective high-order numerical process is gonna be built‎.‎To do this‎, ‎the temporal-fractional derivative of the MI-ADM-TF is discretized by using the linear interpolation‎, ‎and the temporal-first derivative by applying the first-order precision of the finite-difference method‎. ‎On the other hand‎, ‎After obtaining a semi-discrete form‎, ‎to obtain the full-discrete technique‎, ‎the space derivative is approximated utilizing a collocation approach based on the Legendre basis‎.‎The convergence order of the implicit numerical design for MI-ADM-TF is discussed in that is linear‎.‎Moreover‎, ‎the temporal-discretized structure of stability is also discussed theoretically in general in the article‎.‎Eventually‎, ‎two models are offered to demonstrate the quality and authenticity of the established process‎.

This study explores the second-order slip effect on the flow of MHD chemically reacting fluid through an inclined micro-annular channel. As knowledge in flow and heat transfer is showcased in macro/micro-channel areas, consistent advancement is essential to familiar with fundamental phenomena associated. The free convection study encompasses the temperature-dependent viscosity and uniform magnetic field effect. The dimensionless equations governing the flow are modeled and solved semi-analytically via Akbari-Ganji’s Method (AGM). The velocity, energy, concentration and physical characteristics of the flow results are obtained and discussed with the aid of tables and graphs. It is found that a higher value of the slip parameter diminishes the velocity distribution at the annular gap and surfaces, while, the temperature-dependent exponential variability model enhances the fluid velocity.

To solve fractional-order differential equations (FODEs) with Antagana-Baleanu fractional operator (ABFO), an efficient strategy based on variational iteration method (VIM) and natural transform(NT) is given. Natural variational iteration technique is the name of this method (NVIM). This work also investigates the convergence of the solution of general FODEs obtained by the suggested method given the theory of fixed point and Banach spaces. Furthermore, the error analysis of the NVIM solution is also discussed. Two problems are solved to validate and efficacy demonstrate the of the present. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the exact solution. The NVIMs numerical results reveal that the technique is simple to implement and computationally appealing.

In this work, using the determination function, some new kinds of interpolation formulas are presented.These novel formulas are extensions of Lagrange interpolation. Error formula for these new kind of interpolation formulas are obtained. Finally, using these formulas, some new numerical integration formulas in closed-type and open-type are presented. Absolute error of quadrature formulas show the efficiency of the proposed formulas.

In this article, we introduce a new model of the Stewart Platform robot with rotary servo motors that is very cheap to build. First of all, studied a kinematic of the Stewart Platform, and then, with a simple geometric analysis, we’ll find the angles of servo motors for a specified position. Because of using the angular or rotational Servo motors in this model, sensitivity analysis is a crucial point. After sensitivity analysis of the model, we show the sensitivity level of a type of rotary servo in different coordinates x, y, and z.

The 9/11 witnessed the most destructive terrorist assaults in recorded history, and the attacks led to far bloodier conflicts as part of the subsequent war on terror. Terrorism has become the defining issue of International politics of the 21 century. Hence because of the spread of the ideology, the drone together with Information Communication Technology (ICT) contribute to the counter-terrorism mission by providing universal intelligence, surveillance and hostile strike capabilities to control and reduce the recruitment pool of terrorist groups. This paper focuses on Modelling and Analysis of Counter-terrorism using Drone as a control technique with five compartments. The results showed that use of drone to fight against terrorist/insurgency appear to be 80\% significant reduction on their strength, kill leaders, foot soldiers and put the criminal elements in a state of confusion. Finally, the effective counter-terrorist and counter-insurgent depend on drone deployment across the borders for monitoring.