Can an interacting varying Chaplygin gas and tachyonic matter accelerate Universe?

In this paper a possibility to accelerated the expansion of the large scale universe due to interacting varying Chaplygin gas of a specific form and a tachyonic matter is considered. A specific form of the potential and appropriate values of the parameters allow to obtain early tachyonic dark matter with $\omega_{T} \approx 0$ in recent Universe as well. On the other hand, related to the structure of the field equations describing the dynamics of the background we assumed the form of non-gravitational interaction to be given in advance. A sing changeable interaction between dark energy and dark matter is also included due to a huge interest towards it in recent literature. Possible future finite time singularities for cansidered models have been determined to finalize the paper. The study shows that in case of non-interacting model, the fate of the Universe will be either Type II~(The Sudden Singularity), or Type IV~(Generalized Sudden Singularity) singularity. On the other hand, the consideration of $Q=3 b H \rho_{de}$ non-gravitational interaction in addition to Type II and Type IV singularities will induce also Type V~($\omega$-singularity) singularity. Whilst in the model with $Q=3 b q H \rho_{de}$ non-gravitational interaction only Type IV singularity will be observed. Moreover, $2$ forms of the scale factor has been considered separately allowing analytically obtain the behavior of the cosmological parameters without specifying an explicit form of the potential for tachyonic matter.