An application of improved Bernoulli sub-equation function method to the nonlinear conformable time-fractional SRLW equation

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

“…In the literature, rational (G /G)-expansion [14], new extended direct algebraic [18], improved Bernoulli subequation function [19], and modified extended tanh [20] methods include the conformable derivatives. 3 solutions which are trigonometric and hyperbolic are obtained by rational (G /G)-expansion method, 37 solutions which are rational, exponential, trigonometric and hyperbolic are obtained by new extended direct algebraic method, 3 solutions which are rational and exponential are obtained by improved Bernoulli sub-equation function method and 12 solutions which are trigonometric and hyperbolic are obtained by modified extended tanh method.…”

“…An important one of these equations is the fractional SRLW equation. So far, the solutions of the space-time fractional SRLW equation has been investigated by utilizing the sub-equation method [10], functional variable method [11], exp-function method [11], (G /G)-expansion method [11], tanh-coth method [2], tan-cot method [2], sech-csch method [2] and sec-csc method [2], a novel (G /G)-expansion method [12], Riccati equation method [13], rational (G /G)-expansion method [14], improved F -expansion method [15], the extended Jacobi elliptic function expansion method [16], the auxiliary equation method [17], new extended direct algebraic method [18], improved Bernoulli sub-equation function method [19], modified extended tanh method [20], rational exp(−Ω(η))-expansion method [21], (G /G, 1/G)-expansion method [22], extended auxiliary equation mapping method [23], (D α G/G)-expansion method [24], modified Kudryashov method [25], and the fractional (D α ξ G/G)-expansion method [26]. Among these methods, rational (G /G)-expansion, new extended direct algebraic, improved Bernoulli sub-equation function, and modified extended tanh methods include the conformable derivatives.…”

New exact solutions of space-time fractional Schr¨odinger-Hirota equation

“…In this section, we give the fundamental properties of the IBSEFM. This method is direct, significant, advanced algebraic method for establishing reliable exact solutions for both nonlinear and nonlinear fractional partial differential equations [11,12,[18][19][20][21]. We present five main steps of the IBSEFM as follows:…”

“…The conformable derivative operator which is compatible to many real-world problems provides some properties of classical calculus: derivative of the quotient of two functions, the chain rule, the product of two functions [10]. In addition, many techniques have been applied to find exact solutions for conformable nonlinear partial differential equations [11][12][13][14][15][16].…”

Stable soliton solutions to the nonlinear low-pass electrical transmission lines and the Cahn-Allen equation

“…Akbar). method [18], the generalized Kudryashov [19] approach, the homotopy analysis [20] technique, the mean finite difference Monte-Carlo [21] method, the sine-Gordon expansion method [22], the exp(− ( ))expansion method [23], the modified Kudryashov [24] scheme, the Adomian decomposition method [25], the generalized projective Riccati equation method [26], the multi-symplectic Runge-Kutta method [27], the ( ′ ∕ , 1∕ )-expansion method [28], the modified extended tanh method [29,30], the exponential rational function method [31], the generalized rational function method [32], the unified method [33,34,35], the generalized unified method [36,37,38], the modified auxiliary equation method [39,40], the generalized Bernoulli sub-ODE [41,42] method, the improved Bernoulli sub-equation function (IBSEF) method [43,44,45,46,47,48,49,50,51,52] and others [53]. The IB-SEF method is direct, significant and advanced algebraic method for establishing reliable and functional stable soliton solutions to NLEEs.…”