Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

Abstract

Double Laplace transform method is applied to find exact solutions of linear/nonlinear space-time fractional telegraph equations in terms of Mittag-Leffler functions subject to initial and boundary conditions. Furthermore, we give illustrative examples to demonstrate the efficiency of the method.

Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation

“…The method converges to the exact solution if it exists through successive approximations. The nonlinear term in the equation is expanded in terms of Daftardar-Gejji and Jafari polynomials (see [38,39]).…”

Solutions of Two-Dimensional Nonlinear Sine-Gordon Equation via Triple Laplace Transform Coupled with Iterative Method

“…The purpose of this paper, is to apply triple Laplace transform (TLT) and iterative method (IM) developed in [38] to find the exact solution of two-dimensional nonlinear sine-Gordon equation (NLSGE) subject to appropriate initial and boundary conditions. Dhunde and Waghmare in [37,39] applied double Laplace transform iteration method (TLTIM) to solve nonlinear Klein-Gordon and telegraph equations. By this method, the noise terms disappear in the iteration process, and single iteration gives the exact solution.…”

New approximate-analytical solutions for the nonlinear fractional Schrödinger equation with second-order spatio-temporal dispersion via double Laplace transform method

“…The properties of CmDLTr and CpDLTr have been discussed in [Ozzz] and [Adam4], respectively. For γ, δ ∈ (0, 1], let us now define the formula of the inverse fractional double Laplace transform [LDDL1;RdGw] for both conformable and Caputo fractional derivatives, denoted by ( xt γδ ) −1 [ Ψxt γδ (s 1 , s 1 )], as follows: Definition 9. Given an analytic function: Ψxt γδ (s 1 , s 2 ), for all s 1 , s 2 ∈ C and for γ, δ ∈ (0, 1] such that Re{s 1 ≥ η} and Re{s 2 ≥ σ}, where η, σ ∈ , then, the inverse fractional double Laplace transform (IFDLT) can be expressed [mkaabar] as follows:…”