A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a General Discontinuous Kernel

In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has general discontinuous kernel based on position time space. Conditions of the existence uniqueness solution provided through principal form integral equation, Banach fixed point theorem. After applying properties integral, Fr-NMIDE conformed to Volterra–Hammerstein (V-HIE) second kind, with in Hammerstein term continuous Volterra term. Then, using technique separating method, we obtained HIE, where its physical coefficients were variable time. The Toeplitz matrix method (TMM) schemes used obtain algebraic system by studying convergence system. Maple 18 program was implemented present numerical results, along corresponding errors.