Fractional order calculus (FOC) has wide applications in modeling natural behavior of systems related to different areas of engineering including bioengineering, viscoelasticity, electronics, robotics, control theory and signal processing. This thesis aims at modeling a lossy transmission line using fractional order calculus and identifying its parameters. A lossy transmission line is considered where its behavior is modeled by a fractional order transfer function. A semi-infinite lossy transmission line is presented with its distributed parameters R, L, C and ordinary AC circuit theory is applied to find the partial differential equations. Furthermore, applying boundary conditions and the Laplace transformation a generalized fractional order transfer function of the lossy transmission line is obtained. A finite length lossy transmission line terminated with arbitrary load is also considered and its fractional order transfer function has been derived. Next, the frequency responses of lossy transmission lines from their fractional order transfer functions are also derived. Simulation results are presented to validate the frequency responses. Based on the simulation results it can be concluded that the derived fractional order transmission line model is capable of capturing the phenomenon of a distributed parameter transmission line. The achievement of modeling a highly accurate transmission line requires that a realistic account needs to be taken of its parameters. Therefore, a parameter identification technique to identify the parameters of the fractional order lossy transmission line is introduced. Finally, a few open problems are listed as the future research directions. / Controls

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