Abstract
In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.
Highlights
1 Introduction Leibnitz conceived of a fraction in the derivative and it was discovered that fractional calculus (FC) is better suited to model various scientific processes than classical calculus
Fractional differential equations (FDEs) as a part of FC are considered to be the most popular and important tool to describe and model various phenomena in nature such as earthquake nonlinear oscillations, and the involvement of fractional derivatives in fluiddynamic traffic model eliminates the insufficiency arising in the process of continuum traffic flow
We have investigated the solutions of the N–S equations of fractional order with the help of Elzaki transform decomposition method
Summary
Leibnitz conceived of a fraction in the derivative and it was discovered that fractional calculus (FC) is better suited to model various scientific processes than classical calculus. The researchers are motivated because the theory of fractional calculus interprets nature’s truth in an excellent and systematic way [1,2,3] In this connection, the researchers have investigated that fractional calculus of non-integer-order derivatives are very useful in describing numerous problems of scientific value, such as diffusion processes, damping laws and rheology [4,5,6,7,8]. Fractional differential equations (FDEs) as a part of FC are considered to be the most popular and important tool to describe and model various phenomena in nature such as earthquake nonlinear oscillations, and the involvement of fractional derivatives in fluiddynamic traffic model eliminates the insufficiency arising in the process of continuum traffic flow. We have investigated the solutions of the N–S equations of fractional order with the help of Elzaki transform decomposition method.
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