Adaptation of conformable residual series algorithm for solving temporal fractional gas dynamics models

Abstract

In this paper, we introduced, discussed, and investigated analytical-approximate solutions for nonlinear time fractional gas dynamics equations in terms of conformable differential operator. The proposed algorithm relies upon the conformable power series method and residual error of the generalized Taylor series in terms of the conformable sense. This technique provides analytical solutions in the form of rapid and accurate convergent series in terms of the multiple fractional power series with easily computable components. In this direction, error estimation and convergence analysis for solutions of fractional gas dynamics equations are provided as well. Eventually, several physical examples are tested to justify the theoretical portion and give a clear explanation of dynamic systems for the proposed model for different orders of fractional case The obtained numeric-analytic results indicate that the current algorithm is simple, effective, and profitably dealing with the complexity of many nonlinear fractional dispersion problems.