In the present manuscript, a cubic B-spline finite element collocation method has
been used to obtain numerical solutions of the nonlinear time fractional gas dynamics
equation. While the Caputo form is used for the time fractional derivative appearing
in the equation, the L1 discretization formula is applied to the equation in terms of
time. It has been seen that the results of the present study are in agreement with the
those of exact solution. Therefore, the present method can be used as an alternative
and efficient one to find out the numerical solutions of both linear and nonlinear
fractional differential equations available in the literature. In order to control the
accuracy and efficiency of the present method, the error norms L2 and L1 have been
calculated. It is evident that the newly obtained numerical solutions by the present
method can be computed easily with the implementation and effectiveness of the
approach used in the article.
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