Journal
RUSSIAN PHYSICS JOURNAL
Volume 64, Issue 4, Pages 704-716Publisher
SPRINGER
DOI: 10.1007/s11182-021-02371-w
Keywords
analysis on fractals; fractal diffusion equation; group approach; prolongation; invariance; Lie symmetries
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Funding
- Program of Improving Competitiveness of Tomsk State University among Leading International Research and Education Centers
- Program of Improving the TPU's Competitiveness among the Leading World's SResearch and Education Centers
- Russian Foundation for Basic Research [19-41-700004]
- Tomsk Region Grant [19-41-700004]
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This study investigates the symmetry properties of equations with fractal derivatives defined within the framework of F-alpha calculus, based on group analysis of differential equations. The analogs of transformation prolongations of independent and dependent variables are discussed, and the infinitesimal invariance of equations with fractal derivatives is studied through an example of Lie symmetries of a one-dimensional diffusion equation with a fractal time derivative.
Based on the group analysis of differential equations, we consider the symmetry properties of equations with fractal derivatives defined within the framework of F-alpha-calculus. Analogs of the prolongation of transformations of independent and dependent variables are discussed. The infinitesimal invariance of equations with fractal derivatives is studied on an example of the Lie symmetries of the one-dimensional diffusion equation with a fractal time derivative.
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