Studies over the existence of a certain impulse-based fuzzy integrodifferential equations of the Sobolev type

The present investigation employs impulses and a non-local constraint to prove the existence are some various types of abstract differential and integrodifferential equations related to the Sobolev type. Semigroup theory, specifically variants of constant formula, is utilized to get the analytical results for those equations. Furthermore, findings using the Banach fixed point approach were examined using fuzzy numbers with values spanning the \(\mathscr {E}_n\) ${\mathcal{E}}_n$ range, which includes the normal, convex, upper semi-continuous, and compactly supported interval. A description is given for each situation to illustrate the principle.