A new approximate solution of the fractional trigonometric functions of commensurate order to a regular linear system

Djamel Boucherma, Daoud Idiou, Toufik Achour, Mohamed Lotfi Cherrad, Khaled Chettah, Billel Hamadi


This paper introduces a novel approach to the approximate solution of linear differential equations associated with principal fractional trigonometry and the R function. This method proposes a solution that is expressed by adding appropriate fractional linear fundamental functions. Laplace transforms of these functions are irrational. Therefore, we rounded these functions to obtain rational functions in the form of damped cosine, damped sine, cosine, sine and exponential functions. This transformation was achieved by utilizing the concept of fractional commensurate order and, as a result, has direct practical relevance to real-world physics. The precision and effectiveness of the approach are demonstrated through illustrative examples of solving fractional linear systems.


Fractional differential and integral calculus; Fractional trigonometric functions; Irrational transfer function; Regular linear system; R-function

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DOI: http://doi.org/10.11591/ijeecs.v33.i2.pp879-887


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The Indonesian Journal of Electrical Engineering and Computer Science (IJEECS)
p-ISSN: 2502-4752, e-ISSN: 2502-4760
This journal is published by the Institute of Advanced Engineering and Science (IAES) in collaboration with Intelektual Pustaka Media Utama (IPMU).

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