A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions

Abstract

In this work, we study a new nonlinear partial integro‐differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the multivariable Mittag–Leffler function. We also demonstrate the application of our key theorem with an illustrative example.