Fractional order semilinear Volterra integrodifferential equations in Banach spaces

TL;DR

This paper establishes existence conditions for fractional order semilinear Volterra integrodifferential equations in Banach spaces using fractional cosine families and operator theory.

Contribution

It introduces new sufficient conditions for solutions in Banach spaces, leveraging fractional cosine families and fractional powers of operators.

Findings

Established existence results under new conditions

Applied fractional cosine families in the analysis

Extended theory to fractional semilinear equations

Abstract

In this paper, sufficient conditions are established for the existence results of fractional order semilinear Volterra integrodifferential equations in Banach spaces. The results are obtained by using the theory of fractional cosine families and fractional powers of operators.