Abstract
A new fractional derivative with a non-singular kernel involving exponential and trigonometric functions is proposed in this paper. The suggested fractional operator includes as a special case Caputo-Fabrizio fractional derivative. Theoretical and numerical studies of fractional differential equations involving this new concept are presented. Next, some applications to RC-electrical circuits are provided.
Highlights
In the recent decades, the theory of fractional calculus has brought the attention of a great number of researchers in various disciplines
We suggested a fractional derivative involving the kernel function
We studied fractional differential equations via this new concept in both theoretical and numerical aspects
Summary
The theory of fractional calculus has brought the attention of a great number of researchers in various disciplines. These fractional derivatives play an important role for modeling many phenomena in physics As it was mentioned in Caputo and Fabrizio [12], certain phenomena related to material heterogeneities cannot be well-modeled using Riemann-Liouville or Caputo fractional derivatives. Due to this fact, Caputo and Fabrizio [12] suggested a new fractional derivative. Other fractional derivatives with non-singular kernels were introduced by some authors (see e.g., [10, 25,26,27,28,29]).
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