Study on the fractional Sasa–Satsuma equation of optical solitons in optical fibers and telecommunications

This paper applies the extended direct algebraic method (EDAM) for the first time to obtain the soliton solutions of the fractional Sasa–Satsuma equation (FSSE) with the descriptions of two fractional derivatives. To evaluate the optical soliton and some other solutions of the FSSE, the presented research applies the fractional beta and conformable derivatives. As a useful result of this research, several types of solitons have been identified, such as the single soliton, M-shaped, W-shaped, combined dark-bright, smooth dark, sharp dark, dark-bright, anti-bell shaped, and periodic. Among the nonlinear optics fields expanding at the fastest rate are optical solitons. A fundamental equation in the theory of optical fibers and telecommunications is the fractional Sasa–Satsuma equation. The transmission of femtosecond pulses in optical fibers as well as the interaction and propagation of ultrashort pulses in the sub-picosecond or femtosecond region are influenced by this equation. Additionally, the physical properties of the completed solutions are illustrated via contour, 3D, and 2D graphs. The EDAM is a practical and effective technique that offers a variety of avenues for future investigation. The fresh versions of the findings presented here have not been published in the full body of literature before.