A NOVEL PERSPECTIVE TO THE LOCAL FRACTIONAL BIDIRECTIONAL WAVE MODEL ON CANTOR SETS
Kang‐Le Wang
Abstract
In this paper, the bidirectional wave model is described by using the local fractional derivative (LFD) on Cantor sets for the first time. A novel algorithm is established to obtain the exact traveling-wave solution of the non-differential type for the local fractional bidirectional wave model (LFBWM), which is called the local fractional wave method (LFWM). The advantages of the LFWM are simple, efficient and accurate. The LFWM sheds a new light on solving the local fractional wave equations (LFWE) in physics and engineering. Finally, the physical properties of the obtained exact traveling-wave solution of the non-differential type are elaborated by some simulation figures.
Topics & Concepts
Fractional calculusType (biology)MathematicsPerspective (graphical)Mathematical analysisDerivative (finance)Simple (philosophy)Traveling waveApplied mathematicsGeometryPhilosophyEconomicsEcologyBiologyEpistemologyFinancial economicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods in engineering