Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative

Abstract

In this study, residual power series method, namely RPSM, is applied to solve time-fractional Kadomtsev-Petviashvili (K-P) differential equation. In the solution procedure, the fractional derivatives are explained in the conformable sense. The model is solved approximately and the obtained results are compared with exact solutions obtained by the sub-equation method. The results reveal that the present method is accurate, dependable, simple to apply and a good alternative for seeking solutions of nonlinear fractional partial differential equations.

Exact solutions of the Benney–Luke equation via (1/G')-expansion method

“…(1 / ) G -expansion method [6][7][8][9] the Clarkson-Kruskal direct method [10], the auto-Bäcklund transformation method [11], decomposition method [12], homogeneous balance method [13], the first integral method [14], residual power series method [15], collocation method [16], modified Kudryashov method [17], sine-Gordon expansion method [18,19], the improved Bernoulli sub-equation function method, [20] and so on [21][22][23][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Hyperbolic Type Solutions for the Couple Boiti-Leon-Pempinelli System

“…There are several approaches for finding solutions of nonlinear partial differential equations which have been developed and employed successfully. Some of these are a new sub equation method [1], homotopy analysis method [2,3], homotopy-Pade method [4], homotopy perturbation method [5,6], (G ′ /G)-expansion method [7,8], modified variational iteration algorithm-I [9,10,11], sub equation method [12], Variational iteration method with an auxiliary parameter [13,14,15,16], sumudu transform approach [17], (1/G ′ )-expansion method [18,19], variational iteration method [20,21], auto-Bäcklund transformation method [22], Clarkson-Kruskal direct method [23], Bernoulli sub-equation function technique [24], decomposition method [25,26,27,28], modified variational iteration algorithm-II [29,30,31], first integral method [32], homogeneous balance method [33], modified Kudryashov technique [34], residual power series approach [35], collocation method [36], extended rational SGEEM [37], sine-Gordon expansion method [38,39] and many more [40,41,...…”

Exact solutions of (2 + 1)-Ablowitz-Kaup-Newell-Segur equation

“…Scientists have used many methods to find analytical solutions of NPDEs. Some of these methods are new sub equation method [1,2], (1/G ) -expansion method [3,4], Homotopy analysis and Homotopy-Pade methods [5], (G /G)-expansion method [6,7], Variational Iteration Algorithm-I [8], decomposition method [9][10][11], sumudu transform method [12], sub equation method [13,14], collocation method [15], the auto-Bäcklund transformation method [16], the Clarkson-Kruskal (CK) direct method [17], first integral method [18], homogeneous balance method [19], SGEEM [20], residual power series method [21], Modified Kudryashov method [22], sine-Gordon expansion method (SGEM) [23,24] and so on .…”