Artificial intelligent investigations for the dynamics of the bone transformation mathematical model

Abstract

In this study, the stochastic numerical solutions of the fractional myeloma bone disease system (FMBDS) have been presented. The fractional order investigation provides more accurate solutions of the FMBDS. The FMBDS is classified into three dynamics and the solution of each class is presented by using the artificial neural network enhanced by the scale conjugate gradient procedures (ANN-SCGPs). Three different fractional order performances have been used to present the solutions of the FMBDS by applying the ANN-SCGPs. The statics is chosen as 11%, 12% and 77% for training, testing and verification. Twelve number of hidden neurons with input and output layers have been proposed for the FMBDS. The comparison of proposed and reference solutions is performed that shows the accuracy of the ANN-SCGPs. The consistency, validity, precision, and capability of the ANN-SCGPs can be judged based on the state transitions values, regression actions, correlation behaviors, error histograms, and mean square error data.

Keywords

• Fractional order
• Bone transformation
• Myeloma disease
• Scale conjugate gradient procedures
• Artificial neural networks
• Cell dynamics