###### Abstract
Fractional calculus has been used in nearly all domains of science and has been shown to be advantageous in the recent literature [19]. It has been used in areas such as diode modelling [20] and in the modelling of chemical systems, such as to determine ethanol concentration [21]. Different fractional calculus methods and applications have been discussed [22], and the application of fractional calculus to robotic manipulators is one key area to prove its viability. The fractional order models, when compared to integer order models of any real-time system, are much more accurate [23]. As compared to integer order controllers, these provide better responses, as shown in [24]. [PERSON] et al. [25] demonstrate a novel fractional sliding mode control structure  
Figure 1: Classic control strategy based on state estimation methods. for integer and fractional order systems. These studies suggest that such a controller also shows significantly improved accuracy and performance. In [26; 27], a design of a fractional order controller is proposed for the improved response of the transient state of pendulum cart and gantry crane systems. Other examples in which a fractional control strategy has been used to improve system performance include [28]. By using fractional and integer order sliding mode control [29], a comparison study has been conducted with a planer robotic manipulator and has shown a significant improvement in stability. Similarly, in [30], the same control action has been applied to a nonlinear system based on Lyapunov stability, resulting in the rapid convergence of the system to an equilibrium point. [PERSON] et al. [31] presented a Lyapunov stability-based serial robotic manipulator whose controller was based on the fractional Proportional-Derivative-Integral (PID) controller. An effort for the control of a 2 DOF flexible manipulator using a Linear Quadratic Regulator (LQR)-based controller was shown in [32]. Similarly, various other research works that involve the use of fractional order calculus are available, such as the FO sliding mode control of a Single Flexible Link Robotic Manipulator (SFLRM) [33], the use of a super twisting second-order algorithm ensuring robustness and high positional accuracy [34], and the use of discrete sliding Fourier transform to estimate tip deflection [35]. Fractional order controllers have the potential to improve SFLRM responses tremendously. In [36], the authors presented a fractional sliding mode observer based on the state estimation approach. An algorithm was proposed by [PERSON] et al. [37] to choose an appropriate fractional order dynamic model for robotic manipulators. However, to the author's knowledge, the control of a SFLRM and 2 DSFJ using a fractional order PID controller with state estimation techniques is not present in the given literature. Therefore, this paper discusses this method of controller design in order to improve the system performance of robotic manipulators. This work focuses on the estimation of the states of a 2 DSFL and 2 DSFJ using output measurements from encoders present at joints of the robotic manipulator. The research pertains to the fractional control and estimation of the orientation of robotic manipulators for better accuracy and low-cost implementation. This improved accuracy has been a major demand in applications such as laser cutting and CNC, where the first choices of sensors are low-cost accelerometers and encoders. The Bayesian state estimation methods such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Kalman Filter (KF) and particle filter (PF) have been applied to a 2 DOF Serial Flexible Link Robot and 2 DOF Serial Flexible Joint Robot by [PERSON]. The accuracy of the tracking performance and the orientation of the robot are the parameters that have been used for evaluation. The key contributions and highlights in this paper are as follows:  
1. Utilization of joint angle measurements in the filters for state estimations;
2. Implementation of a fractional order PID controller;
3.