Fractional sub-equation method for the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation

Abstract

In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is described in the Jumarie’s modified Riemann-Liouville sense. Two illustrative examples are given, showing the accuracy and convenience of the method.

A novel analytical method for time-fractional differential equations

“…If we compare our solutions with the solutions appeared in literature before [25,26], we can see that our solutions are di¤ererent.…”

New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods

“…Previously, many authors had tackled the fractional Sharma-Tasso-Olver equation in different approaches. For example, finding exact solutions of the fractional Sharma-Tasso-Olver equation in the sense of the modified Riemann-Liouville derivative using the (G /G, 1/G)-expansion method [56], the tanh ansatz method [57], the exp(−Φ(ξ)) method [58], the sub-equation method [59], and the improved extended tanh-coth method [13]. In addition, constructing exact solutions of the nonlinear conformable time Sharma-Tasso-Olver equation via conformable derivatives was done using the simplest equation method [60] and the direct algebraic method [61].…”

A nonlinear fractional Sharma–Tasso–Olver equation: New exact solutions

“…In the same way, the model studied in this work (1.1) have been solved by using the fractional Riccati Equation method [13] and the fractional sub-equation method [14]. Compared with the mentioned methods used to solve the fractional Sharma-Tasso-Olver equation, the technique used here is very simple, effective and gives us more solutions.…”