Solutions of fractional gas dynamics equation by a new technique |
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Authors: | Ali Akgül Alicia Cordero Juan Ramon Torregrosa |
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Institution: | 1. Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, TR-56100 Turkey;2. Instituto de Matemáticas Multidisciplinar, Universitat Politècnica de València, Valencia, 46022 Spain |
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Abstract: | In this paper, a novel technique is formed to obtain the solution of a fractional gas dynamics equation. Some reproducing kernel Hilbert spaces are defined. Reproducing kernel functions of these spaces have been found. Some numerical examples are shown to confirm the efficiency of the reproducing kernel Hilbert space method. The accurate pulchritude of the paper is arisen in its strong implementation of Caputo fractional order time derivative on the classical equations with the success of the highly accurate solutions by the series solutions. Reproducing kernel Hilbert space method is actually capable of reducing the size of the numerical work. Numerical results for different particular cases of the equations are given in the numerical section. |
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Keywords: | fractional gas dynamics equation Hilbert space operators |
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