nonlocal caputo generalized proportional fractional integro-differential systems: an existence study

The objective of this work is to investigate the existence and uniqueness of the solution to a nonlinear fractional integro-differential equation with a non-local condition involving the generalized fractional proportional caputo derivative of two distinct orders. to achieve this, krasnoselskii's fixed point theorem is utilized to examine the existence of the solution, followed by the application of banach's fixed point theorem to study the uniqueness. lastly, two illustrative examples are provided to highlight the main results.