ANALISIS INTEGRAL FRAKSIONAL FUNGSI HIPERBOLIK: KASUS TANGEN DAN COTANGEN: Fractional Integral Analysis of Hyperbolic Function: The Case of Tangent and Cotangent

Janan, Syifaul
Kurniawan, Andro

Al-Aqlu : Jurnal Matematika, Teknik dan Sains
Vol. 4 No. 1 (2026): Januari 2026

This study examines the Riemann-Liouville fractional integral for hyperbolic tangent and cotangent functions with order  using Maclaurin series division method and power function fractional integral theorem. Results show the fractional integral of hyperbolic tangent is expressed as a fractional power series with gamma function coefficients, while hyperbolic cotangent has a singular term . MATLAB visualization shows α variations produce different growth characteristics. Hyperbolic tangent is regular with odd function symmetry, while hyperbolic cotangent is singular around the origin. This research provides explicit formulas for fractional calculus applications