Exact Solutions of Linear Multiple Delay Partial Differential Equations

ABSTRACT This paper develops an analytical framework for linear differential equations with multiple discrete delays. A new function, referred to as the multiple‐delay exponential function, is introduced, and some of its fundamental properties are established. This function is then employed, in conjunction with Fourier transform methods, to derive exact solutions for a class of partial differential equations with multiple delays. These exact solutions highlight how delays affect the dynamics, revealing features that should be considered when applying the studied equations to model physical systems.