Mathematics and engineering analysis for a multi-dimensional, multi-disciplinary world has embraced kinematics, motions, and energy with classical calculus, as well as fractional. Moreover, traditional education physical science and engineering areas are blending and mixing for research and for real design applications. These notes and investigations present intermediate and advanced level treatments with a sprinkling of elementary. The presented calculus has an evolutionary perspective of addressing change, as well as accumulated change in a unified manner to better understand motions and memory described through both quantification and computation. Several original contributions are made on reactive power law fluid flows, on lubrication, on acoustic horn shapes, on dielectric relaxation, as well as on peristaltic pumping. Moreover, new perspectives are given for dissipation contributions in energetics of the motions.