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All Journal Indonesian Journal of Electrical Engineering and Computer Science
Daoud Idiou
Département d’Electronique Université Constantine 1

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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
Indonesian Journal of Electrical Engineering and Computer Science Vol 33, No 2: February 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v33.i2.pp879-887

Abstract

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.
Co-Authors Billel Hamadi Djamel Boucherma Khaled Chettah Mohamed Lotfi Cherrad Toufik Achour