On the fractional functional differential equation with abstract Volterra operator

TL;DR

This paper investigates the existence, uniqueness, and data dependence of solutions to fractional functional differential equations involving abstract Volterra operators, using Picard operators, supported by examples and applications.

Contribution

It introduces a new analysis framework for fractional differential equations with Volterra operators, extending existing methods with novel theoretical results.

Findings

Established conditions for existence and uniqueness of solutions.

Demonstrated data dependence of solutions.

Provided illustrative examples and applications.

Abstract

The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the abstract operator of Volterra, in the context of the Picard operators. We present an example, in order to illustrate the results obtained. We present an application, with the end goal to illustrate the results obtained.