A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

In this work, the existence and uniqueness solution of fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position time-space L2Ω×C0,T, T<1. The FrNMIoDE conformed to Volterra-Hammerstein integral (V-HIE) second kind, after applying characteristics integral, in for Hammerstein term continuous time Volterra (VI) term. Then, using separation technique methodology, we developed HIE, whose physical coefficients were time-variable. By examining system’s convergence, product Nystrom (PNT) associated schemes employed create algebraic system (NAS).