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

## TL;DR

This paper investigates the existence of solutions for certain types of fuzzy integrodifferential equations using mathematical techniques like semigroup theory and fixed point approaches.

## Contribution

The paper introduces a novel approach to proving existence for impulse-based fuzzy integrodifferential equations of the Sobolev type.

## Key findings

- Existence results are derived using semigroup theory and variants of constant formulas.
- The Banach fixed point approach is applied to fuzzy numbers within a specific mathematical range.
- Examples are provided to illustrate the theoretical findings.

## Abstract

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 \documentclass[12pt]{minimal}
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\begin{document}$$\mathscr {E}_n$$\end{document}En range, which includes the normal, convex, upper semi-continuous, and compactly supported interval. A description is given for each situation to illustrate the principle.