Exact solution for the fractional partial differential equation by homo separation analysis method

Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena

“…For all the attention, it is an indispensable task to attain the closed-form wave structures of the fractional differential equations (FDEs). Various meaningful and truthful approaches have been interpolated for achieving the closed-form wave structures of FDEs, including the -expansion approach [4,5], extended Jacobi elliptic function expansion method [6], improved sub-equation scheme [7], modified fractional reduced differential transform method [8], sub-equation method [9], singular manifold method [10], fractional homotopy method [11], fractional reduced differential transform method [12], modified ( ′/ ) G G -expansion approach [13], extended modified mapping method [14], Sine-Gordon expansion method [15], extended trial equation method [16], iterative method [17], simplest equation method [18], ansatz scheme [19], F-expansion method [20], modified Kudryashov method [21], extended mapping method [22], homo separation analysis method [23], modified simple equation method [24], reduced differential transform scheme [25], modified extended mapping method [26], functional variable method [27], extended direct algebraic method [28], Darcy's law rule [29], function transformation method [30], the variation of ( ′/ ) G G -expansion method [31], differential transform method [32], unified scheme, ( ′/ ) G G -expansion approach [33,34], Kudryashov method [35], new extended Kudryashov process [36], Sine-cosine approach [37], auxiliary equation scheme [38] and many other techniques…”