The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter
. The parameter
allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter
depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter
. Moreover, the efficiency and reliability of this technique are verified by the numerical examples.
With 25% confirmed cases of the country’s total number of coronavirus disease 2019 (COVID-19) on 31 January 2021, Jakarta has the highest confirmed cases of in Indonesia. The city holds a significant role as the centre of government and national economic activity for which pandemic have had a huge impact. Spatiotemporal analysis was employed to identify the current condition of disease transmission and to provide comprehensive information on the COVID-19 outbreak in Jakarta. We applied space-time analysis to visualise the pattern of COVID-19 hotspots in each time series. We also mapped area capacity of the referral hospitals covering the entire area of Jakarta to understand the hospital service range. This research was conducted in 4 stages: i) disease mapping; ii) spatial autocorrelation analysis; iii) space-time pattern analysis; and iv) areal capacity mapping. The analysis resulted in 144 sub-districts categorised as high vulnerability. Autocorrelation studies by Moran’s I identified cluster patterns and the emerging hotspot results indicated successful interventions as the number of hotspots fell in the first period of social restrictions. The results presented should be beneficial for policy makers.