Novel analytical approach to modified fractal gas dynamics model with the variable coefficients
Kang‐Le Wang
2022ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik35 citationsDOIOpen Access PDF
Abstract
Abstract In this study, the modified fractal gas dynamics model (GDM) with variable coefficients is successfully represented using the fractal derivative. We obtain the fractal variational principle of the modified fractal GDM by employing the fractal semi‐inverse method. Based on the established fractal variational principle, a new and fascinating algorithm is presented to solve the fractal model, which is called fractal two‐scale variational method (FTSVM). Finally, two numerical examples are given to indicate the efficiency and accuracy of the proposed algorithm. The FTSVM sheds a new light on the fractal differential equations.
Topics & Concepts
FractalFractal derivativeMathematicsFractal landscapeFractal analysisFractal dimension on networksInverseApplied mathematicsVariable (mathematics)Variational principleStatistical physicsMathematical analysisFractal dimensionPhysicsGeometryFractional Differential Equations SolutionsNonlinear Waves and SolitonsDifferential Equations and Numerical Methods