(eng): In this work, we study a new nonlinear partial integro-differential equation withnonlocal initial value conditions and investigate the solutions of this equation.By considering an equivalent implicit integral equation via series, we provethe uniqueness of solutions of the equation by Babenko's approach, Banach'scontraction principle, and the multivariable Mittag–Leffler function. We alsodemonstrate the application of our key theorem with an illustrative example.