Abstarct: Abstract The design and development of advanced and active prostheses for lower limbs represents a significant revolution in the field of biomedical engineering, aiming to increase mobility, improve quality of life, and enable a return to daily activities for individuals with limb deficiencies. Despite significant advancements in this field, these prostheses still face numerous challenges such as complex and highly nonlinear dynamics, uncertainties in modeling, and undesirable behaviors in actuators including phenomena like hysteresis and dead zones, all of which can have significant negative impacts on the quality of walking and user comfort. In this regard, this thesis addresses the development of advanced control methods for active lower-limb prostheses with the aim of effectively isolating vibrations and accelerations caused by foot-ground impact from the soft tissue of the residual limb. In this thesis, a novel and comprehensive control frxamework tixtled "Dynamic Fractional Order Terminal Sliding Mode Controller with Disturbance Observer-baxsed Approach for Active Shock-Absorbing Lower Limb Prostheses" is presented. This controller is designed to effectively isolate unwanted vibrations and accelerations that are transmitted from various parts of the prosthesis, especially the pylon and foot, to the residual soft tissue in the limb during movement. The unique feature of using fractional calculus in this controller ensures a much faster convergence rate to the desired equilibrium state, and also significantly reduces the chattering phenomenon, which is a common problem in sliding mode control. The designed fractional sliding surfaces, by utilizing the memory properties of fractional derivatives, improve the controller's performance in the face of model uncertainties and external disturbances. Among the most important parts of this research is the development and implementation of a disturbance observer that accurately estimates and effectively compensates for uncertainties and nonlinear behaviors caused by actuators and real operating conditions of the system. One of the significant innovations of this research is the dehighly nonlinear dynamics, uncertainties in modeling, and undesirable behaviors in actuators including phenomena like hysteresis and dead zones, all of which can have significant negative impacts on the quality of walking and user comfort. In this regard, this thesis addresses the development of advanced control methods for active lower-limb prostheses with the aim of effectively isolating vibrations and accelerations caused by foot-ground impact from the soft tissue of the residual limb. In this thesis, a novel and comprehensive control frxamework tixtled "Dynamic Fractional Order Terminal Sliding Mode Controller with Disturbance Observer-baxsed Approach for Active Shock-Absorbing Lower Limb Prostheses" is presented. This controller is designed to effectively isolate unwanted vibrations and accelerations that are transmitted from various parts of the prosthesis, especially the pylon and foot, to the residual soft tissue in the limb during movement. The unique feature of using fractional calculus in this controller ensures a much faster convergence rate to the desired equilibrium state, and also significantly reduces the chattering phenomenon, which is a common problem in sliding mode control. The designed fractional sliding surfaces, by utilizing the memory properties of fractional derivatives, improve the controller's performance in the face of model uncertainties and external disturbances. Among the most important parts of this research is the development and implementation of a disturbance observer that accurately estimates and effectively compensates for uncertainties and nonlinear behaviors caused by actuators and real operating conditions of the system. One of the significant innovations of this research is the design of a high-order disturbance observer, which is capable of estimating the derivative of accumulated disturbances and, by reducing the controller gain, allows for reduced energy consumption and increased actuator lifespan. This feature is very important for active prostheses that require long-term operation. In this research, a detailed and comprehensive analysis of system stability using Lyapunov theory is presented, which guarantees the robustness and reliable performance of the proposed controller under various operating conditions. Extensive simulation studies have been conducted to evaluate the performance of the proposed controller under ideal and non-ideal conditions. The mathematical model used is a six-mass system including the foot and pylon, socket, soft and hard tissues of the residual limb, and the upper body, which models the complete dynamics of the prosthesis-human system. The ground reaction force is modeled non-linearly, considering the viscoelastic properties of the materials. The results of these simulations clearly demonstrate the significant superiority of the proposed controller compared to conventional classical sliding mode control and dynamic sliding mode control baxsed on observers. This superiority is evident in more effective vibration isolation, a noticeable reduction in unwanted accelerations, and an overall improvement in the quality and comfort of walking for prosthesis users. Furthermore, the frequency analysis of the system indicates that the proposed controller provides optimal performance in the 8-18 Hz frequency range, which has high human sensitivity according to ISO 2631. The use of an appropriate frequency weighting filter allows for an accurate evaluation of the controller's performance under real conditions. The results of this research show that the proposed controller has excellent capability in advancing active prosthetic technology and increasing walking comfort and efficiency for amputees. The results of this research indicate that combining fractional calculus with dynamic sliding mode control provides a novel and efficient approach for controlling complex systems with multiple uncertainties. The proposed method not only has a strong theoretical foundation but also possesses the capability for practical implementation on embedded systems.