Approximate Analytical Solution of Two-Dimensional Nonlinear Time-Fractional Damped Wave Equation in the Caputo Fractional Derivative Operator
Open Access
- 4 November 2022
- journal article
- research article
- Published by Hindawi Limited in Mathematical Problems in Engineering
- Vol. 2022, 1-28
- https://doi.org/10.1155/2022/7004412
Abstract
In this work, we proposed a new method called Laplace-Pade-Caputo fractional reduced differential transform method (LPCFRDTM) for solving a two-dimensional nonlinear time-fractional damped wave equation subject to the appropriate initial conditions arising in various physical models. LPCFRDTM is the amalgamation of the Laplace transform method (LTM), Pade approximant, and the well-known reduced differential transform method (RDTM) in the Caputo fractional derivative senses. First, the solution to the problem is gained in the convergent power series form with the help of the Caputo fractional-reduced differential transform method. Then, the Laplace-Pade approximant is applied to enlarge the domain of convergence. The advantage of this method is that it solves equations simply and directly without requiring enormous amounts of computational work, perturbations, or linearization, and it expands the convergence domain, leading to the exact answer. To confirm the effectiveness, accuracy, and convergence of the proposed method, four test-modeling problems from mathematical physics nonlinear wave equations are considered. The findings and results showed that the proposed approach may be utilized to solve comparable wave equations with nonlinear damping and source components and to forecast and enrich the internal mechanism of nonlinearity in nonlinear dynamic events.Keywords
This publication has 49 references indexed in Scilit:
- Numerical inverse Laplace homotopy technique for fractional heat equationsThermal Science, 2018
- New function method to the (n+1)-dimensional nonlinear problemsAn International Journal of Optimization and Control: Theories & Applications (IJOCTA), 2017
- Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé ApproximationActa Physica Polonica A, 2017
- Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equationsJournal of King Saud University - Engineering Sciences, 2017
- A new technique of Laplace Pade reduced differential transform method for (1 3) dimensional wave equationsNew Trends in Mathematical Science, 2017
- Approximate solutions of coupled Ramani equation by using RDTM with compared DTM and exact solutionsNew Trends in Mathematical Science, 2016
- Adomian Decomposition Method Combined with Padé Approximation and Laplace Transform for Solving a Model of HIV Infection of CD4+T CellsDiscrete Dynamics in Nature and Society, 2015
- Analytical approximations of two and three dimensional time-fractional telegraphic equation by reduced differential transform methodEgyptian Journal of Basic and Applied Sciences, 2014
- Modified Reduced Differential Transform Method for Partial Differential-Algebraic EquationsJournal of Applied Mathematics, 2014
- The existence and convergence of subsequences of Padé approximantsJournal of Mathematical Analysis and Applications, 1973