The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink-type, bright, dark, and singular soliton solutions are reported, and several numerical simulations are also included. The calculations are carried out by Maple software. All of the solutions that are derived in this paper are believed to be new and have presumably not been reported in earlier publications.
In this study, a novel mathematical model based on third-order nonlinear multisingular functional differential equations (MS-FDEs) is presented. e designed model is solved by using a well-known differential transformation (DT) scheme that is a very credible tool for solving the nonlinear third-order nonlinear MS-FDEs. In order to check the exactness, efficacy, and convergence of the scheme, some numerical examples are presented based on nonlinear third-order MS-FDEs and numerically solved by using DT scheme. e scheme of differential transformation allows us to find a complete solution and a closed approximate solution of the differential equation. e distinctive advantage of the computational technique is to deal with the complex and monotonous physical problems that are obtained in various branches of engineering and natural sciences. Moreover, a comparison of the obtained numerical outcomes from the exact solutions shows the correctness, accurateness, and exactness of the designed model as well as the presented scheme.
In this work, we make use of the conformable fractional differential transform method (CFDTM) in order to compute an approximate solution of the fractional-order susceptible-infected-recovered (SIR) epidemic model of childhood disease. The method provides the solution in the form of a rapidly convergent series. Two explanatory and illustrative examples are given to represent the efficacy of the obtained results. KEYWORDS childhood disease, conformable fractional differential transform method (CFDTM), fractional-order susceptible-infected-recovered (SIR) epidemic model, fractional power series, Liouville-Caputo fractional derivative Math Meth Appl Sci. 2019;42:935-941.wileyonlinelibrary.com/journal/mma
In this paper, we have extended the Fractional Differential Transform method for the numerical solution of the system of fractional partial differential-algebraic equations. The system of partial differential-algebraic equations of fractional order is solved by the Fractional Differential Transform method. The results exhibit that the proposed method is very effective.
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