Rational solutions of the Toda lattice equation in Casoratian form

Soliton solutions of coupled systems by improved (Gʹ/G)-expansion method

“…Besides, the improved (G /G)-expansion method handles NLEEs in a direct manner with no initial/boundary conditions requirement. It is to be highlighted that (G /G)-expansion method may be considered another form of expfunction method as mentioned in [33][34][35][36]. Moreover numerical results consists of cases 1-4 can be obtained by taking δ u + u = 0 as auxiliary equation, however cases 5,6 can only be determined by making use of auxiliary equation mentioned in Eq.…”

Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

“…Among those, we can name: Hirota's bilinear method, [10] Casoratian technique, [11] homotopy perturbation method, [12] ADM-Padé technique, [13] etc. But, most of the methods are not easy to handle and require a thorough knowledge of the solution procedure one has in mind.…”

Construction of exact solutions for fractional-type difference-differential equations via symbolic computation

“…As far as we could verify, relatively less work is being performed for the symbolic computation of exact solutions to fractional-type DDEs while there has been a considerable amount of work done in finding exact solutions to polynomial DDEs. In the last decade, due to the increased interest in DDEs, a whole range of analytical solution methods such as Hirota's bilinear method [16], ADM-Padé technique [17], Casoratian technique [18], homotopy perturbation method [19], Exp-function method [20], and so on. were developed by the researchers.…”