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Evolution of Temporal Fractional Derivative due to Spatial Stochastic Disorder in Transport Phenomena

Shantanu Das


This paper formulates a particular problem of transport in a disordered heterogeneous media and brings out the ‘mathematical process’ to get a fractional order differential equation in time; to get spatial heterogeneity, embedded as stochastic process. This pure mathematical process of evolution of constituent law as Fractional Differential Equation of transport gives better insight to the disordered relaxation and transportmechanism; as compared to earlier descriptive approaches, based on experimental observation, based on fractal dimensions of disorder or via memory integral and its convolutions or based on Fractional Brownian Motion, and statistical wait times and jumps.


functional, functional derivative, telegraph random field, fractional derivative

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