Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods

A Note on Conformable Double Laplace Transform and Singular Conformable Pseudoparabolic Equations

“…Recently, several researchers applied the conformable Laplace transform method to solve different types of fractional differential equation (see [15,16]). Many exact solutions in various wave forms for the nonlinear conformable time-fractional parabolic equation with exponential nonlinearity are formally constructed in [17]. e goal of this paper is to investigate the solution of singular conformable fractional pseudoparabolic equation and conformable coupled pseudoparabolic equation by conformable double Laplace transform decomposition methods (CDLTDMs).…”

Solution of singular one-dimensional Boussinesq equation by using double conformable Laplace decomposition method

“…The space-time fractional Boussinesq equations in Caputo sense derivatives are studied by using the homotopy perturbation method [12]. The authors in [13] discussed the nonlinear conformable problem by using the exp(-φ(ε))-expansion and modified Kudryashov methods. In the present study, the new conformable fractional double Laplace transform decomposition method is recommended for developing the solutions of singular Boussinesq equation.…”

Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method

“…And so far a lot of effective methods have been developed and used by many authors. For example, these methods include the finite difference method [6], the ( / ) method [7][8][9][10], the Jacobi elliptic function method [11], the projective Riccati equation method [12], the modified Kudryashov method [13][14][15][16][17][18][19], the exp method [20][21][22][23][24][25], the ansatz method [26], the first integral method [27][28][29], and the subequation method [30][31][32][33][34]. Based on these methods, a lot of fractional partial differential equations have been investigated.…”