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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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1865-7109
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Volume 69, Issue 10-11

Issues

Fractional Transmission Line with Losses

José Francisco Gómez-Aguilar
  • Corresponding author
  • Department of Solar Materials, Renewable Energy Institute, National Autonomous University of Mexico, Priv. Xochicalco s/n. Col. Centro, Temixco Morelos, Mexico
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Baleanu Dumitru
  • Department of Solar Materials, Renewable Energy Institute, National Autonomous University of Mexico, Priv. Xochicalco s/n. Col. Centro, Temixco Morelos, Mexico
  • Cancaya University, Faculty of Art and Sciences, Department of Mathematics and Computer Sciences, Balgat 0630, Ankara, Turkey c Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia
  • Institute of Space Sciences, P.O. Box MG-23, R 76900, Magurele-Bucharest, Romania
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-03-19 | DOI: https://doi.org/10.5560/zna.2014-0049

Abstract

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.

Keywords : Transmission Line; Fractional Calculus; Caputo Derivative; Fractional Components

About the article

Received: 2014-01-23

Revised: 2014-06-02

Published Online: 2015-03-19

Published in Print: 2014-11-01


Citation Information: Zeitschrift für Naturforschung A, Volume 69, Issue 10-11, Pages 539–546, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.5560/zna.2014-0049.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung.

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[1]
Tahereh Bashiri, S. Mansour Vaezpour, and Juan J. Nieto
Journal of Function Spaces, 2018, Volume 2018, Page 1
[2]
J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, and V. H. Olivares-Peregrino
Advances in Mathematical Physics, 2016, Volume 2016, Page 1
[3]
José Gómez-Aguilar, Victor Morales-Delgado, Marco Taneco-Hernández, Dumitru Baleanu, Ricardo Escobar-Jiménez, and Maysaa Al Qurashi
Entropy, 2016, Volume 18, Number 8, Page 402
[4]
J. F. Gómez Aguilar, T. Córdova-Fraga, J. Tórres-Jiménez, R. F. Escobar-Jiménez, V. H. Olivares-Peregrino, and G. V. Guerrero-Ramírez
Mathematical Problems in Engineering, 2016, Volume 2016, Page 1
[5]
J. F. Gómez-Aguilar, J. E. Escalante-Martínez, C. Calderón-Ramón, L. J. Morales-Mendoza, M. Benavidez-Cruz, and M. Gonzalez-Lee
Advances in Mathematical Physics, 2016, Volume 2016, Page 1
[6]
José Gómez-Aguilar, Huitzilin Yépez-Martínez, Celia Calderón-Ramón, Irene Cruz-Orduña, Ricardo Escobar-Jiménez, and Victor Olivares-Peregrino
Entropy, 2015, Volume 17, Number 9, Page 6289
[7]
J.F. Gómez-Aguilar, H. Yépez-Martínez, C. Calderón-Ramón, M. Benavidez-Cruz, and L.J. Morales-Mendoza
Journal of Electromagnetic Waves and Applications, 2016, Volume 30, Number 2, Page 259

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