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.