For all the attention, it is an indispensable task to attain the closed-form wave structures of the fractional differential equations (FDEs). For example, the fluid-dynamic traffic model could succeed the deficiency based upon the hypothesis of continuum traffic flow, the principles of fractional calculus could model the dynamical methods in fluids and porous structures and fractional derivatives can form the nonlinear oscillation of earthquake. Nature and research problems and most of the life and compound phenomena are explained and invented through fractional wave models. New ideas in physics including astrophysics, computational physics, fluid dynamic, mathematical physics, biological physics and medical physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics.
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