fractional model

The mathematical fractional modeling of TiO_2 nanopowder synthesis by sol–gel method at low temperature

Titanium dioxide is a compound of oxygen and titanium with the formula TiO$_2$ present in nature and manufactured on an industrial scale.  It is used in several fields and applications such as cosmetics, paint, food, photocatalyst, electrodes in lithium batteries, dye solar cells (DSSC), biosensors, etc., given its importance and its various fields of application, there are several methods of synthesis of TiO$_2$ such as the sol–gel method widely used to obtain nanoparticles.  In our study, on the one hand we synthesized titanium dioxide nanopowders crystallized in the