Abstract:
Bangladesh isoneofthemostovercrowdedanddenselypopulatedcountriesglobally.Thus,in recent years, the population problem has been a great concern of the policymakers ofBangladesh.Forthedevelopmentandprogressofthecountry,itwouldbecrucialtoperceiveand estimate the increasing trend of the population. This research work principally focuses on theanalysis through data fitting using the nonlinear least square curve fitting method andforecastofthefuturepopulationgrowthofthecountry byconsideringmathematicalmethods. Available actual and adjusted census data (1974-2022) of Bangladesh populationapplied in the well-known autonomous logistic population growth model and fund that alldata sets of logistic (exact), deterministic (Adam-Bashforths-Multon predictor-corrector(PECE) method), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach,and logistic multi-scaling approximation fits with a good agreement. Again the existenceand uniqueness of the solution for deterministic and fractional-order and Hyers-Ulamstabilityhavebeenstudied.Generally,thegrowthrateandcarryingcapacityofthepopulationofanycountryslowlyfluctuatewithtime.Thisanalysisprovidesseveraladvantages to assessing an approximate closed-form of straightforward solutions, as mostprevious studies conducted with population models of single species employed constantgrowth rates and carrying capacity, and no fractional-order method is studied. Finally, ourprojectionadhereswithanexcellentagreementtotheestimate(2012-2061)oftheBangladesh Ministry of Planning and Bureau of Statistics (BBS). Thus, we bank on thefindingsofthisresearch workwillassistinsuccessfulpopulationforecastandplanning,development,and progression ofthe nation.