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

In this paper, two relatively modern analytical-numerical techniques, the generalized differential transform method (GDTM) and its reduced differential transform method (RDTM), are considered 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, a comparative study is presented between the proposed methodologies, while the behavior of approximation is shown graphically for different values of fractional-order α in term of Caputo sense. Our numerical investigations indicate that the RDTM is very simple, more accurate and effective than the GDTM.