Families of propagating soliton solutions for (3+1)-fractional Wazwaz-BenjaminBona-Mahony equation through a novel modification of modified extended direct algebraic method

Abstract

The article presents a new modification to the modified Extended Direct Algebraic Method (mEDAM) namely r+mEDAM to effectively and precisely acquire propagating soliton and other travelling wave solutions to the Fractional Wazwaz-Benjamin-Bona-Mahony (FWBBM) equation. By using this updated approach, we are able to find more and new families of propagating soliton solutions for the FWBBM problem, such as soliton, kink, lump-like singular, trigonometric, hyperbolic, periodic, shock, singular & non-singular wave solutions. We also provide 3D and 2D graphs that visually illustrate the obtained solutions. By obtaining accurate propagating soliton solutions, our r+mEDAM proves to be practical while also revealing important details about the dynamics of the equation and suggesting possible applications in the fields of optics, materials research, and water waves.

Fractional Fokas-Lenells equation: analyzing travelling waves via advanced analytical method

“…In a variety of research publications, powerful approaches have been created for the investigation of exact solutions. These methods include, the modified extended direct algebraic method [21][22][23], the Riccati-Bernoulli sub-ODE method [24,25], the fractional functional method [26], the extended trail equation scheme [27], the modified simple equation method [28], the fractional (G G¢)-expansion [29], the ansatz scheme [30,31], and the fractional exp-function method [32]. The first integral scheme [33] and the functional variable scheme [34] are two different schemes that researchers have used for soliton solutions of the space-time nonlinear conformable fractional differential equations, such as Bogoyavlenskii, the Schrödinger-Hirota, and the modified KDV-Zakharov-Kuznetsov equations.…”