In this paper, we consider some linear/nonlinear differential equations (DEs) containing conformable derivative operator. We obtain approximate solutions of these mentioned DEs in the form of infinite series which converges rapidly to their exact values by using and homotopy analysis method (HAM) and modified homotopy perturbation method (MHPM). Using the conformable operator in solutions of different types of DEs makes the solution steps are computable easily. Especially, the conformable operator has been used in modelling DEs and identifying particular problems such as biological, engineering, economic sciences and other some important fields of application. In this context, the aim of this study is to solve some illustrative linear/nonlinear problems as mathematically and to compare the exact solutions with the obtained solutions by considering some plots. Moreover, it is an aim to show the authenticity, applicability, and suitability of the methods constructed with the conformable operator.

Unmanned Aerial Vehicles (UAVs) are widely used in fields such as autonomous missions, reconnaissance, surveillance, and various industrial applications. These vehicles can perform desired tasks without human intervention in challenging environmental conditions. However, UAV control can be difficult due to environmental factors, wind disturbances, and uncertainties in system parameters. Therefore, developing reliable control strategies for UAVs is a significant challenge for researchers and engineers. This study presents a comprehensive review of rotary-wing UAVs, focusing on quadcopter and helicopter systems. Approximately 77 studies were selected from the Web of Science (WOS) database and analyzed, with an emphasis on Sliding Mode Control (SMC) and Fractional-Order SMC (FOSMC) applications in these systems. The review addresses key topics such as degrees of freedom, proposed control methods, adjustment techniques, comparative methods, fractional-order definitions, simulation tools, and explanations. The literature analysis highlights current research trends by showing the performance advantages and limitations of SMC and FOSMC methods. Furthermore, future research directions and existing knowledge gaps are discussed in detail. This review was prepared to provide the control engineering community with a comprehensive understanding of SMC and FOSMC applications in rotary wing systems and to contribute to the development of innovative and effective control strategies.

Challenging and time-consuming tasks performed by humans can today be performed faster and more efficiently by robot manipulators with the development of technology. Robotic manipulators are flexible, can fit in small spaces, and are very effective for tasks that require high precision. They are widely used in the production lines of factories (handling, assembly, welding, etc.) and in fields that require manpower, such as medicine and engineering. Since it is used in tasks that require precision, its control is also important. Sliding modal control (SMC), one of the robust control methods, is a control method used in nonlinear systems because it can be applied to unstable systems, is easy to design and, has high accuracy against parameter uncertainties. However, it produces an unstable control signal within a certain range and this discontinuous control signal causes cracking in the system, which causes damage to the system elements. Especially in recent years, one of the most recent and successful methods used to reduce the chattering effect, which is the biggest problem in the SMC approach, is the fractional order design of the sliding surface. In the fractional order SMC (FOSMC) method, the derivative expression in the sliding surface is defined using the system variable’s error to be controlled and the derivative of the error is computed fractionally. In this paper, Caputo FOSMC (CFOSMC), defined with 3 different sliding surfaces using the Caputo fractional operator, is compared with classical SMC for controlling a 2-degree of-freedom (2-DOF) robot manipulator. According to the results obtained from simulation comparisons, it is observed that approach 3 gives better results than the other two approaches and classical SMC in terms of overshoot, settling and error value for some derivative orders.