In the present study, a design of a fractional order mathematical model is presented based on the schistosomiasis disease. To observe more accurate performances of the results, the use of fractional order derivatives in the mathematical model is introduce based on the schistosomiasis disease is executed. The preliminary design of the fractional order mathematical model focused on schistosomiasis disease is classified as follows: uninfected with schistosomiasis, infected with schistosomiasis, recovered from infection, susceptible snail unafflicted with schistosomiasis disease and susceptible snail afflicted with this disease. The solutions to the proposed system of the fractional order mathematical model will be presented using stochastic artificial neural network (ANN) techniques in conjunction with the Levenberg-Marquardt backpropagation (LMBP), referred to as ANN-LMBP. To illustrate the preciseness of the ANN-LMBP method, mathematical presentations of three different values focused on fractional order will be performed. These statics performances are taken in these investigations are 78% and 11% for both learning and certification. The accuracy of the ANN-LMBP method is determined by comparing the values obtained by the database Adams-Bash forth-Moulton scheme. The simulation-based error histograms (EHs), MSE, recurrence, and state transitions (STs) will be offered to achieve the capability, accuracy, steadiness, abilities, and finesse of the ANN-LMBP method.