On the transcendental solutions of Fermat type delay-differential and c-shift equations with some analogous results

TL;DR

This paper investigates finite order transcendental entire solutions of Fermat type delay-differential and c-shift equations, extending previous results and providing new examples to support the findings.

Contribution

It introduces the first analysis of finite order transcendental solutions for these specific Fermat type equations, improving and extending earlier research.

Findings

Identified conditions for solutions to exist

Extended previous results in the literature

Provided examples illustrating key assertions

Abstract

In this paper, we mainly investigate on the finite order transcendental entire solutions of two Fermat types delay-differential and one Fermat type c-shift equations, as these types were not considered earlier. Our results improve those of [13] in some sense. In addition, we also extend some recent results obtained in [18]. A handful number of examples have been provided by us to justify our certain assertion as and when required.