Riemann-Liouville Fractional Cosine Functions

TL;DR

This paper introduces the concept of Riemann-Liouville fractional cosine functions, establishing their equivalence to fractional resolvents, thereby advancing the theoretical framework of fractional calculus.

Contribution

It presents a new notion of fractional cosine functions and proves their equivalence to existing fractional resolvents, enriching the mathematical theory.

Findings

Riemann-Liouville fractional cosine functions are defined.

Proved equivalence to fractional resolvents.

Enhances understanding of fractional calculus structures.

Abstract

In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $\alpha$-order fractional cosine function is equivalent to Riemann-Liouville $\alpha$-order fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math. Nachr. 288, No. 7, 784-797 (2015)].