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- Title
Analytic Solution of the Langevin Differential Equations Dominated by a Multibrot Fractal Set.
- Authors
Ibrahim, Rabha W.; Baleanu, Dumitru
- Abstract
We present an analytic solvability of a class of Langevin differential equations (LDEs) in the asset of geometric function theory. The analytic solutions of the LDEs are presented by utilizing a special kind of fractal function in a complex domain, linked with the subordination theory. The fractal functions are suggested for the multi-parametric coefficients type motorboat fractal set. We obtain different formulas of fractal analytic solutions of LDEs. Moreover, we determine the maximum value of the fractal coefficients to obtain the optimal solution. Through the subordination inequality, we determined the upper boundary determination of a class of fractal functions holding multibrot function ...(z) = 1 + 3k z + z³.
- Subjects
LANGEVIN equations; STOCHASTIC differential equations; FRACTALS; FRACTAL analysis; ANALYTIC functions
- Publication
Fractal & Fractional, 2021, Vol 5, Issue 2, p1
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract5020050