Dynamic equations on time scales constitute a unified framework that bridges continuous and discrete analysis by treating differential and difference equations within a single theory. A time scale is ...

Ordinary differential equations (ODEs), difference equations and dynamical systems provide complementary frameworks for modelling the evolution of quantities in continuous or discrete time. ODEs ...

In the past few decades, the use of phase field-modeling equations for mathematical modeling has progressed. Phase separation has been studied extensively in thermodynamics and materials engineering, ...