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Z. Naturforsch. 69a, 539 – 546
(2014)
doi:10.5560/ZNA.2014-0049
Fractional Transmission Line with Losses
1 Department of Solar Materials, Renewable Energy Institute, National Autonomous University of Mexico, Priv. Xochicalco s/n. Col. Centro, Temixco Morelos, Mexico
2 Cancaya University, Faculty of Art and Sciences, Department of Mathematics and Computer Sciences, Balgat 0630, Ankara, Turkey
3 Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia
4 Institute of Space Sciences, P.O. Box MG-23, R 76900, Magurele-Bucharest, Romania
Received January 23, 2014 / revised June 2, 2014 / published online August 13, 2014
Reprint requests to: J. F. G.; E-mail:
jgomez@ier.unam.mx
In this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. Two cases are solved, with fractional spatial and fractional temporal derivatives, and also numerical simulations were carried out, where there are taken both derivatives in simultaneous form. Two parameters σx and σt are introduced and a physical relation between these parameters is reported. Solutions in space and time are given in terms of the Mittag–Leffler functions. The classic cases are recovered when β and γ are equal to 1.
Key words: Transmission Line; Fractional Calculus; Caputo Derivative; Fractional Components.