Solving fractional system of partial differential equations with parameters derivative by combining the GDTM and RDTM

Abstract

In this paper, we consider two relatively modern analytical-numerical techniques, the generalized differential transform method (GDTM) and its reduced differential transform method (RDTM), for treating a class of coupled fractional system of partial differential equations with parameters derivative arising in fluid-mechanics, acoustics and gas-dynamic. The methods provide appropriate representation of the solutions in convergent series formula with accurately computable components via the RDTM and with costly components via the GDTM. In this regards, comparative study is presented between the proposed methodologies, while the behavior of approximation is shown graphically for different values of fractional-order  in term of Caputo sense. Our numerical investigations indicate that the RDTM is very simple, more accurate and effective than the GDTM.