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Shareholders' Equity and Share-Based Payments (Details) - USD ($)
3 Months Ended 6 Months Ended
Mar. 31, 2022
Mar. 31, 2021
Mar. 31, 2022
Mar. 31, 2021
Sep. 30, 2021
Aug. 27, 2020
Share-Based compensation            
Common stock, shares authorized 75,000,000   75,000,000   75,000,000  
Preferred stock, shares authorized 10,000,000   10,000,000   10,000,000  
Share-based compensation expense $ 204,589 $ 204,574 $ 250,180 $ 250,165    
2019 Plan            
Share-Based compensation            
Common stock, shares authorized 139,691   139,691      
Share-based compensation expense $ 204,589 204,574 $ 250,180 250,165    
Number of shares of common stock reserved for awards 663,751   663,751      
Unrecognized compensation cost, related to non-vested stock options $ 73,828   $ 73,828      
2019 Plan | Maximum            
Share-Based compensation            
Number of shares of common stock reserved for awards 750,000   750,000      
2019 Plan | Employee            
Share-Based compensation            
Share-based compensation expense $ 44,594 44,594 $ 90,185 90,185    
Number of shares of common stock reserved for awards 300,000   300,000      
2019 Plan | Chief Financial Officer            
Share-Based compensation            
Number of shares of common stock available for awards under the plan           100,000
2019 Plan | Non Employee Director            
Share-Based compensation            
Share-based compensation expense $ 159,995 $ 159,980 $ 159,995 $ 159,980