PoS(BPU11)169 Fractional calculus in modelling hereditariness and nonlocality in transmission lines Dušan Zorica, ,,∗ Stevan M. Cvetićanin  and Milan R. Rapaić   Department of Physics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, Serbia  Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, Beograd, Serbia  Department of Power,Electronic and Telecommunication Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, Serbia  Department of Computing and Control Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića, 6, Novi Sad, Serbia E-mail: dusan.zorica@df.uns.ac.rs, stevan.cveticanin@uns.ac.rs, rapaja@uns.ac.rs Transmission lines are traditionally modelled by considering Heaviside’s elementary circuit that contains a resistor and inductor in the series branch, accounting for the energy losses and magnetic effects, while the shunt branch contains a resistor and a capacitor, accounting for the energy losses and capacitive phenomena. Classical telegrapher’s equations, modelling the signal propagation in a transmission line, are obtained by assuming the infinitesimal length of the elementary circuit and by passing to a continuum. The generalization of elementary circuit is two-fold: topological by adding the capacitor in the series branch in order to account for the charge accumulation effects along the line and constitutive in order to account for the memory effects that transmission line may display. The constitutive generalization is performed by changing the constitutive relation describing the capacitive and inductive material properties using the fractional calculus approach accounting for the short-tail memory. On the other hand, the inclusion of nonlocal material properties of a transmission line is performed by considering the magnetic coupling of inductors in the series branch of Heaviside’s elementary circuit, so that the magnetic flux is obtained as a superposition of local and constitutively given nonlocal magnetic flux through the cross-inductivity kernel. Signal propagation is studied in the case of power, exponential, and Gauss type cross- inductivity kernels. The presented results are published in [1–3]. 11th International Conference of the Balkan Physical Union (BPU11), 28 August - 1 September 2022 Belgrade, Serbia ∗ Speaker © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/