# Time fractional advection-dispersion equation

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## Abstract

A time fractional advection-dispersion equation is obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0<α<-1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional advection-dispersion equation.

## AMS Mathematics Subject Classification

26A33 49K20 44A10## Key words and phrases

time fractional advection-dispersion equation Mellin transform Laplace transform## References

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© Korean Society for Computational and Applied Mathematics 2003