The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.
In this study, we establish exact solutions of fractional Kawahara equation by using the idea of -expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.
We use the fractional derivatives in modified Riemann-Liouville derivative sense to construct exact solutions of time fractional simplified modified Camassa-Holm (MCH) equation. A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and, as a result, many exact analytical solutions are obtained with more free parameters. When these free parameters are taken as particular values, the traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. Moreover, the numerical presentations of some of the solutions have been demonstrated with the aid of commercial software Maple. The recital of the method is trustworthy and useful and gives more new general exact solutions.
The double diffusion heat transfer phenomenon for the unsteady viscous fluid has been focused subject to the non-Fourier relations. The thermal radiation impact along the inclined direction has also been utilized. The non-Fourier analysis for the heating phenomenon is performed using the Cattaneo–Christov and Fick’s mathematical models. The transformed systems due to similarity variables are analytically predicted via HAM scheme and also with the assistance of BVP4C solver. The convergence of the method to justify a solution is also observed. Also, the effect of involved physical parameters on the given model is explained through graphs and tables. The observations are compared with the available literature with a fine agreement. The numerical representation and quantitative analysis for drag force, heat transfer and mass transfer rates are worked out.
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