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This paper presents a fractional-order framework for control of blood pressure regulation system. A new perspective is explored to control the blood pressure in lieu of the conventional control framework. A multi-variable scenario is adopted to control two outputs: mean arterial blood pressure (MABP) and cardiac output (CO) simultaneously. Three fractional-order controllers are designed and tuned optimally for the multi-input multi-output (MIMO) blood pressure regulation system. To test the effectiveness of the designed fractional controllers, control investigations are carried out based on controller performance indices and sensitivity performance indices. Stability analysis and sensitivity analysis are carried out in order to assure stable as well as robust feedback design. Sensitivity analysis of the paper reveals the controller's ability to handle model uncertainties of the blood pressure regulation system. Numerical simulation results of the paper unfold the best suitable fractional-order controller for the enhanced closed-loop performance of the blood pressure regulation system.