Special Session 129: Qualitative and Quantitative Techniques for Differential Equations arising in Economics, Finance and Natural Sciences
Contents
We study time-space fractional advection-dispersion (FADE) equation and
time-space fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role
in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into partial
differential equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent
solutions based on optimal system are investigated which constitute the exact solutions of
original fractional differential equations.