The development of novel fractional order differentiators and their applications

The primary goal of this study is to look into the analysis, design, and applications of fractional order digital differentiators and integrators. First, different existing procedures for the calculation of the Rational Approximation of the fractional-order operator, s α are explored. The discretization of s α , is a crucial step in the construction of digital differentiators and integrators. The s to z transformations used in this investigation, including those by Al-Alaoui, Tahar, and Gujan Stancic, are reviewed. Direct and indirect discretization methods can be used to design fractional order digital differentiators and integrators. This paper discusses the development of fractional order differentiators and integrators of order α using the indirect discretization technique. The created fractional order differentiators have been used in the processing of Electro Cardio Gram (ECG) Signal and localization of edges in an Image. The reported findings are being compared to standard approaches. All simulations are performed using MATLAB. The Root Mean Square Error (RMSE) Values obtained using Guran Stancic Transform based Fractional Order Differentiator for the detection of the Edges in an Image is 0.0014265. The Signal to Noise Ratio (SNR) Values obtained using Al-Alaoui Transform based Fractional Order Differentiator for the detection of the Edges in an Image is − 108 . 9501 dB. • A Study of the existing Rational Approximations is Performed. • Novel s to z transforms is explored. • Indirect Discretization is Followed. • New Formulae for Fractional Order Differentiators is derived. • Edges in an Image and QRS Complexes is detected.