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Solutions of fractional gas dynamics equation by a new technique
Author(s) -
Akgül Ali,
Cordero Alicia,
Torregrosa Juan Ramon
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5950
Subject(s) - mathematics , reproducing kernel hilbert space , hilbert space , kernel (algebra) , fractional calculus , representer theorem , series (stratigraphy) , space (punctuation) , mathematical analysis , kernel method , kernel embedding of distributions , pure mathematics , computer science , paleontology , artificial intelligence , support vector machine , biology , operating system
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.