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Mechanism of Wave Dissipation via Memory Integral vis-à-vis Fractional Derivative

Shantanu Das


The wave dissipation is a complex mechanism. Here the dissipation mechanism is explained as convolution integral with a memory kernel, and its relation to fractional wave equation in time and space. New parameters of dimensions of time and length are introduced to indicate the presence of fractional derivative in time and space respectively. A normalized solution to fractional order wave equation is obtained where the time (space) scales are normalized via non dissipative wave’s periodic time period and wave length, where the fractional order of time and space fractional derivative is ratio of the square of this new parameter to the time period and wave length of non dissipating periodic wave. The explanation is given for wave dissipation mechanism via memory integrals with different kernels and its relation to fractional order differential equation for relaxation kinetics in space and time.


Wave Equation, Memory Integral, Dissipation, Fractional Derivative, Mittag-Leffler

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