Recently, the development of neural network method for solving differential equations has made a remarkable progress for solving fractional differential equations. In this paper, a neural network method is employed to solve time-fractional telegraph equation. The loss function containing initial/boundary conditions with adjustable parameters (weights and biases) is constructed. Also, in this paper, a time-fractional telegraph equation was formulated as an optimization problem. Numerical examples with known analytic solutions including numerical results, their graphs, weights, and biases were also discussed to confirm the accuracy of the method used. Also, the graphical and tabular results were analyzed thoroughly. The mean square errors for different choices of neurons and epochs have been presented in tables along with graphical presentations.

In this study, the heat relocation properties of quadratic thermal radiation and quadratic convective unsteady stagnation point flow of electro-magnetic Sutterby nanofluid past a spinning sphere under zero mass flux and convective heating conditions are investigated. The governing equations are developed and expressed as partial differential equations, which are afterwards transformed into ordinary differential equations by applying similarity conversion. In the investigation, the JAX library in Python is employed with the numerical approach to artificial neural networks. It is investigated to what extent physical characteristics affect primary and secondary velocity, temperature, and concentration fields. The results demonstrate that due to increasing unsteadiness, Sutterby fluid, and magnetic field parameters, the flow of Sutterby nanofluid in the flow zone accelerates in the primary (x-direction) and slows down in the rotational (z-direction). The outcome also shows that an increase in the quadratic radiation parameter, the magnetic field constraint, and the electric field constraint induce increases in the temperature distribution of the Sutterby nanofluid. The study also shows that the concentration of nanoparticles decreases with increasing Lewis numbers and unsteadiness parameter values. Additionally, a graph illustrating the mean square error is investigated and provided.