Citation: Fadhal, E.; Akbulut, A.; Kaplan, M.; Awadalla, M.; Abuasbeh, K. Extraction of Exact Solutions of Higher Order Sasa-Satsuma Equation in the Sense of Beta Derivative. Symmetry 2022, 14, 2390. https:// doi.org/10.3390/sym14112390 Academic Editors: Ji-Huan He, Muhammad Nadeem and Ioan Ra¸ sa Received: 10 October 2022 Accepted: 5 November 2022 Published: 11 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). symmetry S S Article Extraction of Exact Solutions of Higher Order Sasa-Satsuma Equation in the Sense of Beta Derivative Emad Fadhal 1 , Arzu Akbulut 2 , Melike Kaplan 3 , Muath Awadalla 1, * and Kinda Abuasbeh 1 1 Department of Mathematics and Statics, Collage of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia 2 Department of Mathematics, Art-Science Faculty, Uludag University, 16059 Bursa, Turkey 3 Department of Computer Engineering, Faculty of Engineering and Architecture, Kastamonu University, 37150 Kastamonu, Turkey * Correspondence: mawadalla@kfu.edu.sa Abstract: Nearly every area of mathematics, natural, social, and engineering now includes research into finding exact answers to nonlinear fractional differential equations (NFDES). In order to discover the exact solutions to the higher order Sasa-Satsuma equation in the sense of the beta derivative, the paper will discuss the modified simple equation (MSE) and exponential rational function (ERF) approaches. In general, symmetry and travelling wave solutions of the Sasa-Satsuma equation have a common correlation with each other, thus we reduce equations from wave transformations to ordinary differential equations with the help of Lie symmetries. Actually, we can say that wave moves are symmetrical. The considered procedures are effective, accurate, simple, and straightforward to compute. In order to highlight the physical characteristics of the solutions, we also provide 2D and 3D plots of the results. Keywords: beta derivative; sasa satsuma equation; wave transformations; exact solutions PACS: 02.30 Jr; 02.70.Wz; 04.20.Jb 1. Introduction Nowadays, academic researchers deal with many physical phenomena in plasma physics, physical chemistry, geophysics, fluid mechanics, nonlinear optics, electromagnetic theory, and fluid motion, and their mathematical models are expressed by NFDEs [1,2]. These equations are commonly used in various scientific disciplines and have been investi- gated from different viewpoints [3]. The exact solutions of these equations have gained more and more interest. For this reason, a lot of different techniques have been dealt with by researchers. Among this research, the following ones can be listed, for instance, Hosseini et al. derived new exact solutions of a new (4+1)-dimensional Burgers equation [4]. Dehin- gia et al. applied the Hopf-bifurcation [5]. Mirzazadeh et al. worked on the second-order nonlinear Schrödinger equation with weakly nonlocal and parabolic laws [6]. Aktar et al. obtained the soliton solutions of a biological model [7]. Mathanaranjan et al. applied the sinh-Gordon procedure [8]. Jannat et al. constructed different types of travelling wave solutions for the considered equation by employing the Auto-Backlund transformations [9]. Ala et al. applied the improved Bernoulli sub-equation function procedure [10]. Kaplan and Akbulut utilized the modified Kudryashov approach [11], Hosseini et al. used the homotopy analysis method (HAM) [12], Mahmood et al. utilized discrete fractional opera- tors [13], Mohammed et al. employed discrete CF-fractional operators [14], Arshed et al. utilized the modified auxiliary equation (MAE) method [15]. The limit relationships between solitary wave solutions and periodic wave solutions, which correspond to the outer and inner trajectories of asymmetric homoclinic trajectories, were explored by the authors in [16]. We deal with the wave transformations, which Symmetry 2022, 14, 2390. https://doi.org/10.3390/sym14112390 https://www.mdpi.com/journal/symmetry