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## Electromagnetic waves described by a fractional derivative of variable and constant order with non singular kernel

 1 Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa, Anand-388421, Gujarat, India 2 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa

* Corresponding author: Krunal B. Kachhia

Received  March 2019 Published  September 2020

The concept of differential operator with variable order has attracted attention of many scholars due to their abilities to capture more complexities like anomalous diffusion. While these differential operators are useful in real life, they can only be handled numerically. In this work, we used a newly introduced variable order differential operators that can be used analytically and numerically, has connection with all integral transform to model some interesting mathematical models arising in electromagnetic wave in plasma and dielectric. The differential operators used are non-singular and have the crossover properties therefore the models studied can explain the propagation of the wave in two different layers which cannot be achieved with those differential variable order operators with singular kernels. Using the Laplace transform and its connection with the new differential operator, we derive the exact solution of the models under investigation.

Citation: Krunal B. Kachhia, Abdon Atangana. Electromagnetic waves described by a fractional derivative of variable and constant order with non singular kernel. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020172
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