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, ...

This paper aims to demonstrate a numerical strategy via finite difference formulations for time fractional reaction–diffusion models which are ubiquitous in chemical and biological phenomena. The time ...

STFEs simulate various physical phenomena that exhibit anomalous diffusion or non-local behavior. Solitons, which are solitary wave solutions that maintain their shape while propagating at constant ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...