In this document, we are keen on showing the rough scientific answers for fragmentary differential conditions by utilizing the Vieta-Lucas polynomial procedure. The fractional derivatives have represented in the Caputo sense. The implementation identified with the Vieta-Lucas strategy has been produced for differential conditions to the degree of admittance to estimated scientific arrangements of frameworks of partial differential conditions. The arrangements of our model conditions are determined as concurrent series with effectively process-able segments. A few models are tackled as representations, utilizing emblematic calculation. The mathematical outcomes show that the methodology is not difficult to carry out and exact with implementation to frameworks of fragmentary differential conditions. The strategy presented a hopeful device for addressing numerous direct and nonlinear partial differential conditions