LTI Kapasitor ve Konformal Kesirli Mertebeden Türev Kullanılarak Modellenmiş Kapasitör ile İki Kapasitör Problemi

Abstract

Fractional order circuit elements have been started to model different types of circuit elements, circuits and systems in the last decades. There are different types of fractional derivatives. Recently, a new simple fractional derivative method called“conformable fractional derivative” has been brought out. It is simpler than other fractional derivatives and has already been used tomodel supercapacitors. It is important to model the new circuit elements and analyze the circuits containing them so that they can be exploited at their full potential. Two capacitor problem is a famous problem in physics and circuit theory. In this study, a new two capacitor problem a circuit which consists of an LTI capacitor and a supercapacitor which has been modelled with conformable fractional derivative have been examined. The differential equations which describe the circuit have been derived. The circuit current is found explicitly however the voltages of the capacitors do not have analytical solutions. That’s why they are solved numerically.